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baunsgaard pushed a commit to branch master
in repository https://gitbox.apache.org/repos/asf/systemds.git

commit e8da72fa0c607fe191265a962f39b79420d06611
Author: baunsgaard <[email protected]>
AuthorDate: Fri May 14 10:13:40 2021 +0200

    [SYSTEMDS-2992] CLA init workload cost functions
    
    Initial version of cost based co-coding functions.
    This commit adds costs for compressed tsmm and compressed mm.
---
 .../runtime/compress/CompressedMatrixBlock.java    |   2 +
 .../compress/CompressedMatrixBlockFactory.java     |  17 +-
 .../runtime/compress/CompressionSettings.java      |   8 +-
 .../compress/CompressionSettingsBuilder.java       |  15 +-
 .../runtime/compress/CompressionStatistics.java    |  18 +-
 .../runtime/compress/cocode/AColumnCoCoder.java    |   6 +-
 .../runtime/compress/cocode/CoCodeBinPacking.java  |   4 +-
 .../sysds/runtime/compress/cocode/CoCodeCost.java  |   4 +-
 .../compress/cocode/CoCodeCostMatrixMult.java      |  72 ++--
 .../runtime/compress/cocode/CoCodeStatic.java      |   4 +-
 .../runtime/compress/cocode/PlanningCoCoder.java   |  16 +-
 .../sysds/runtime/compress/colgroup/AColGroup.java |  16 +-
 .../compress/colgroup/ColGroupCompressed.java      |   8 +-
 .../runtime/compress/colgroup/ColGroupConst.java   |   5 -
 .../runtime/compress/colgroup/ColGroupDDC.java     |   5 +-
 .../runtime/compress/colgroup/ColGroupEmpty.java   |   4 -
 .../runtime/compress/colgroup/ColGroupFactory.java | 102 ++---
 .../runtime/compress/colgroup/ColGroupOLE.java     |   7 +-
 .../runtime/compress/colgroup/ColGroupOffset.java  |  10 +-
 .../runtime/compress/colgroup/ColGroupSDC.java     |   2 +-
 .../compress/colgroup/ColGroupSDCSingle.java       |   2 +-
 .../compress/colgroup/ColGroupSDCSingleZeros.java  |  20 +-
 .../compress/colgroup/ColGroupSDCZeros.java        |  16 +-
 .../runtime/compress/colgroup/ColGroupSizes.java   |  57 ++-
 .../compress/colgroup/ColGroupUncompressed.java    |   5 +
 .../runtime/compress/colgroup/ColGroupValue.java   |  66 +--
 .../compress/colgroup/dictionary/ADictionary.java  |  36 +-
 .../compress/colgroup/dictionary/Dictionary.java   |  22 +
 .../colgroup/dictionary/DictionaryFactory.java     | 135 +++++-
 .../colgroup/dictionary/MatrixBlockDictionary.java | 456 +++++++++++++++++++++
 .../compress/colgroup/dictionary/QDictionary.java  |  10 +
 .../colgroup/dictionary/SparseDictionary.java      | 218 ----------
 .../compress/estim/CompressedSizeEstimator.java    |  87 +++-
 .../estim/CompressedSizeEstimatorExact.java        |   3 +-
 .../estim/CompressedSizeEstimatorFactory.java      |  41 +-
 .../estim/CompressedSizeEstimatorSample.java       |  38 +-
 .../compress/estim/CompressedSizeInfoColGroup.java |  27 +-
 .../sysds/runtime/compress/lib/BitmapEncoder.java  |  56 +--
 .../runtime/compress/lib/BitmapLossyEncoder.java   |  30 +-
 .../runtime/compress/lib/CLALibLeftMultBy.java     |   2 +-
 .../runtime/compress/lib/CLALibRightMultBy.java    |   6 +-
 .../sysds/runtime/compress/lib/CLALibSquash.java   |  11 +-
 .../sysds/runtime/compress/utils/Bitmap.java       |  29 +-
 .../utils/{Bitmap.java => MultiColBitmap.java}     |  43 +-
 .../org/apache/sysds/utils/MemoryEstimates.java    |   2 +
 .../compress/AbstractCompressedUnaryTests.java     |   3 -
 .../component/compress/CompressedTestBase.java     |   7 +-
 .../compress/CompressibleInputGenerator.java       |  15 +
 .../sysds/test/component/compress/TestBase.java    |  13 +-
 .../test/component/compress/TestConstants.java     |   1 +
 .../compress/colgroup/JolEstimateTest.java         |  74 ++--
 .../compress/estim/SampleEstimatorTest.java        | 119 ++++++
 52 files changed, 1314 insertions(+), 661 deletions(-)

diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlock.java 
b/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlock.java
index bb7781e..249ad3e 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlock.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlock.java
@@ -208,6 +208,7 @@ public class CompressedMatrixBlock extends MatrixBlock {
                ret.allocateDenseBlock();
                decompress(ret);
 
+               ret.examSparsity();
                if(DMLScript.STATISTICS || LOG.isDebugEnabled()) {
                        double t = time.stop();
                        LOG.debug("decompressed block w/ k=" + 1 + " in " + t + 
"ms.");
@@ -256,6 +257,7 @@ public class CompressedMatrixBlock extends MatrixBlock {
                ret.allocateDenseBlock();
                decompress(ret, k);
 
+               ret.examSparsity();
                if(DMLScript.STATISTICS || LOG.isDebugEnabled()) {
                        double t = time.stop();
                        LOG.debug("decompressed block w/ k=" + k + " in " + 
time.stop() + "ms.");
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlockFactory.java
 
b/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlockFactory.java
index bb0cf8a..1756018 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlockFactory.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/CompressedMatrixBlockFactory.java
@@ -28,6 +28,7 @@ import org.apache.commons.lang3.tuple.Pair;
 import org.apache.commons.logging.Log;
 import org.apache.commons.logging.LogFactory;
 import org.apache.sysds.runtime.compress.cocode.PlanningCoCoder;
+import 
org.apache.sysds.runtime.compress.cocode.PlanningCoCoder.PartitionerType;
 import org.apache.sysds.runtime.compress.colgroup.AColGroup;
 import org.apache.sysds.runtime.compress.colgroup.ColGroupConst;
 import org.apache.sysds.runtime.compress.colgroup.ColGroupEmpty;
@@ -161,18 +162,18 @@ public class CompressedMatrixBlockFactory {
                        _stats.estimatedSizeCols = sizeInfos.memoryEstimate();
 
                logPhase();
-               long memoryEstimate = sizeInfos.memoryEstimate();
 
-               if(memoryEstimate < _stats.originalSize)
+               if(_stats.estimatedSizeCols < _stats.originalSize || 
compSettings.columnPartitioner == PartitionerType.COST_MATRIX_MULT)
                        coCodePhase(sizeEstimator, sizeInfos, mb.getNumRows());
                else {
-                       LOG.info("Estimated Size of singleColGroups: " + 
memoryEstimate);
+                       LOG.info("Estimated Size of singleColGroups: " + 
_stats.estimatedSizeCols);
                        LOG.info("Original size                    : " + 
_stats.originalSize);
                }
        }
 
        private void coCodePhase(CompressedSizeEstimator sizeEstimator, 
CompressedSizeInfo sizeInfos, int numRows) {
                coCodeColGroups = 
PlanningCoCoder.findCoCodesByPartitioning(sizeEstimator, sizeInfos, numRows, k, 
compSettings);
+               _stats.estimatedSizeCoCoded = coCodeColGroups.memoryEstimate();
                logPhase();
        }
 
@@ -206,6 +207,7 @@ public class CompressedMatrixBlockFactory {
 
        private void compressPhase() {
                res.allocateColGroupList(ColGroupFactory.compressColGroups(mb, 
coCodeColGroups, compSettings, k));
+               _stats.compressedInitialSize = res.getInMemorySize();
                logPhase();
        }
 
@@ -229,6 +231,7 @@ public class CompressedMatrixBlockFactory {
                        o.add(combineConst(c));
 
                res.allocateColGroupList(o);
+
                logPhase();
        }
 
@@ -276,12 +279,11 @@ public class CompressedMatrixBlockFactory {
        private void cleanupPhase() {
 
                res.cleanupBlock(true, true);
-               mb.cleanupBlock(true, true);
 
                _stats.size = res.estimateCompressedSizeInMemory();
                
                final double ratio = _stats.getRatio();
-               if(ratio < 1) {
+               if(ratio < 1 && compSettings.columnPartitioner != 
PartitionerType.COST_MATRIX_MULT)  {
                        LOG.info("--dense size:        " + _stats.denseSize);
                        LOG.info("--original size:     " + _stats.originalSize);
                        LOG.info("--compressed size:   " + _stats.size);
@@ -291,6 +293,8 @@ public class CompressedMatrixBlockFactory {
                        return;
                }
 
+               mb.cleanupBlock(true, true);
+
                _stats.setColGroupsCounts(res.getColGroups());
 
                logPhase();
@@ -311,10 +315,12 @@ public class CompressedMatrixBlockFactory {
                        switch(phase) {
                                case 0:
                                        LOG.debug("--compression phase " + 
phase + " Classify  : " + getLastTimePhase());
+                                       LOG.debug("--Individual Columns 
Estimated Compression: " + _stats.estimatedSizeCols);
                                        break;
                                case 1:
                                        LOG.debug("--compression phase " + 
phase + " Grouping  : " + getLastTimePhase());
                                        LOG.debug("Grouping using: " + 
compSettings.columnPartitioner);
+                                       LOG.debug("--Cocoded Columns estimated 
Compression:" + _stats.estimatedSizeCoCoded);
                                        break;
                                case 2:
                                        LOG.debug("--compression phase " + 
phase + " Transpose : " + getLastTimePhase());
@@ -324,6 +330,7 @@ public class CompressedMatrixBlockFactory {
                                        LOG.debug("--compression phase " + 
phase + " Compress  : " + getLastTimePhase());
                                        LOG.debug("--compression Hash 
collisions:" + DblArrayIntListHashMap.hashMissCount);
                                        DblArrayIntListHashMap.hashMissCount = 
0;
+                                       LOG.debug("--compressed initial actual 
size:" + _stats.compressedInitialSize);
                                        break;
                                case 4:
                                        LOG.debug("--compression phase " + 
phase + " Share     : " + getLastTimePhase());
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/CompressionSettings.java 
b/src/main/java/org/apache/sysds/runtime/compress/CompressionSettings.java
index ddbc60b..895600d 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/CompressionSettings.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/CompressionSettings.java
@@ -97,10 +97,15 @@ public class CompressionSettings {
         */
        public final EnumSet<CompressionType> validCompressions;
 
+       /**
+        * The minimum size of the sample extracted.
+        */
+       public final int minimumSampleSize;
+
        protected CompressionSettings(double samplingRatio, boolean 
allowSharedDictionary, String transposeInput,
                boolean skipList, int seed, boolean investigateEstimate, 
boolean lossy,
                EnumSet<CompressionType> validCompressions, boolean 
sortValuesByLength, PartitionerType columnPartitioner,
-               int maxColGroupCoCode, double coCodePercentage) {
+               int maxColGroupCoCode, double coCodePercentage, int 
minimumSampleSize) {
                this.samplingRatio = samplingRatio;
                this.allowSharedDictionary = allowSharedDictionary;
                this.transposeInput = transposeInput;
@@ -113,6 +118,7 @@ public class CompressionSettings {
                this.columnPartitioner = columnPartitioner;
                this.maxColGroupCoCode = maxColGroupCoCode;
                this.coCodePercentage = coCodePercentage;
+               this.minimumSampleSize = minimumSampleSize;
                LOG.debug(this);
        }
 
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/CompressionSettingsBuilder.java
 
b/src/main/java/org/apache/sysds/runtime/compress/CompressionSettingsBuilder.java
index 216267e..83d01e5 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/CompressionSettingsBuilder.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/CompressionSettingsBuilder.java
@@ -43,6 +43,7 @@ public class CompressionSettingsBuilder {
        private PartitionerType columnPartitioner;
        private int maxStaticColGroupCoCode = 10000;
        private double coCodePercentage = 0.01;
+       private int minimumSampleSize = 2000;
 
        private final static double defaultSampleRate = 0.01;
 
@@ -255,6 +256,18 @@ public class CompressionSettingsBuilder {
        }
 
        /**
+        * Set the minimum sample size to extract from a given matrix, this 
overrules the sample percentage if the sample
+        * percentage extracted is lower than this minimum bound.
+        * 
+        * @param minimumSampleSize The minimum sample size to extract
+        * @return The CompressionSettingsBuilder
+        */
+       public CompressionSettingsBuilder setMinimumSampleSize(int 
minimumSampleSize) {
+               this.minimumSampleSize = minimumSampleSize;
+               return this;
+       }
+
+       /**
         * Create the CompressionSettings object to use in the compression.
         * 
         * @return The CompressionSettings
@@ -262,6 +275,6 @@ public class CompressionSettingsBuilder {
        public CompressionSettings create() {
                return new CompressionSettings(samplingRatio, 
allowSharedDictionary, transposeInput, skipList, seed,
                        investigateEstimate, lossy, validCompressions, 
sortValuesByLength, columnPartitioner,
-                       maxStaticColGroupCoCode, coCodePercentage);
+                       maxStaticColGroupCoCode, coCodePercentage, 
minimumSampleSize);
        }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/CompressionStatistics.java 
b/src/main/java/org/apache/sysds/runtime/compress/CompressionStatistics.java
index 5c7d815..466953a 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/CompressionStatistics.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/CompressionStatistics.java
@@ -31,10 +31,16 @@ import org.apache.sysds.runtime.compress.colgroup.AColGroup;
  */
 public class CompressionStatistics {
 
+       // sizes while compressing
+       public long estimatedSizeCoCoded;
+       public long estimatedSizeCols;
+       public long compressedInitialSize;
+
+       // sizes before compression
        public long originalSize;
        public long denseSize;
-       public long estimatedSizeColGroups;
-       public long estimatedSizeCols;
+
+       // compressed size
        public long size;
 
        private Map<String, int[]> colGroupCounts;
@@ -74,20 +80,20 @@ public class CompressionStatistics {
 
                for(String ctKey : colGroupCounts.keySet())
                        sb.append(ctKey + ":" + colGroupCounts.get(ctKey)[0] + 
" ");
-               
+
                return sb.toString();
        }
 
        public String getGroupsSizesString() {
                StringBuilder sb = new StringBuilder();
 
-               for(String ctKey : colGroupCounts.keySet()) 
+               for(String ctKey : colGroupCounts.keySet())
                        sb.append(ctKey + ":" + colGroupCounts.get(ctKey)[1] + 
" ");
-               
+
                return sb.toString();
        }
 
-       public double getRatio(){
+       public double getRatio() {
                return (double) originalSize / size;
        }
 
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/AColumnCoCoder.java 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/AColumnCoCoder.java
index 1ede652..124e3a4 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/cocode/AColumnCoCoder.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/cocode/AColumnCoCoder.java
@@ -32,12 +32,10 @@ public abstract class AColumnCoCoder {
 
        final protected CompressedSizeEstimator _est;
        final protected CompressionSettings _cs;
-       // final protected int _numRows;
 
-       protected AColumnCoCoder(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs, int numRows) {
+       protected AColumnCoCoder(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs) {
                _est = sizeEstimator;
                _cs = cs;
-               // _numRows = numRows;
        }
 
        /**
@@ -57,7 +55,7 @@ public abstract class AColumnCoCoder {
        protected CompressedSizeInfoColGroup 
joinWithAnalysis(CompressedSizeInfoColGroup lhs,
                CompressedSizeInfoColGroup rhs) {
                int[] joined = Util.join(lhs.getColumns(), rhs.getColumns());
-               return _est.estimateCompressedColGroupSize(joined);
+               return _est.estimateCompressedColGroupSize(joined,( 
lhs.getNumVals() + 1) * (rhs.getNumVals() + 1));
        }
 
        protected CompressedSizeInfoColGroup 
joinWithoutAnalysis(CompressedSizeInfoColGroup lhs,
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeBinPacking.java 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeBinPacking.java
index 0116edc..e6dace1 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeBinPacking.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeBinPacking.java
@@ -46,8 +46,8 @@ public class CoCodeBinPacking extends AColumnCoCoder {
         */
        public static double BIN_CAPACITY = 0.000032;
 
-       protected CoCodeBinPacking(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs, int numRows) {
-               super(sizeEstimator, cs, numRows);
+       protected CoCodeBinPacking(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs) {
+               super(sizeEstimator, cs);
        }
 
        @Override
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCost.java 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCost.java
index 66ad209..3f7185a 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCost.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCost.java
@@ -49,8 +49,8 @@ public class CoCodeCost extends AColumnCoCoder {
 
        private final static int toSmallForAnalysis = 64;
 
-       protected CoCodeCost(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs, int numRows) {
-               super(sizeEstimator, cs, numRows);
+       protected CoCodeCost(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs) {
+               super(sizeEstimator, cs);
                largestDistinct = Math.min(4096, Math.max(256, (int) 
(sizeEstimator.getNumRows() * cs.coCodePercentage)));
        }
 
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCostMatrixMult.java
 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCostMatrixMult.java
index 910c94a..836e4d0 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCostMatrixMult.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeCostMatrixMult.java
@@ -26,28 +26,35 @@ import java.util.PriorityQueue;
 import java.util.Queue;
 
 import org.apache.sysds.runtime.compress.CompressionSettings;
-import org.apache.sysds.runtime.compress.colgroup.AColGroup.CompressionType;
 import org.apache.sysds.runtime.compress.estim.CompressedSizeEstimator;
+import org.apache.sysds.runtime.compress.estim.CompressedSizeEstimatorSample;
 import org.apache.sysds.runtime.compress.estim.CompressedSizeInfo;
 import org.apache.sysds.runtime.compress.estim.CompressedSizeInfoColGroup;
 
-/**
- * Column group partitioning by number of distinct items estimated. This 
allows us to join columns based on the worst
- * case estimate of the joined sizes. Then once we decide to join, if the 
worst case is okay, we then analyze the actual
- * cardinality of the join.
- * 
- * This method allows us to compress many more columns than the BinPacking
- * 
- */
 public class CoCodeCostMatrixMult extends AColumnCoCoder {
 
-       protected CoCodeCostMatrixMult(CompressedSizeEstimator e, 
CompressionSettings cs, int numRows) {
-               super(e, cs, numRows);
+       protected CoCodeCostMatrixMult(CompressedSizeEstimator e, 
CompressionSettings cs) {
+               super(e, cs);
        }
 
        @Override
        protected CompressedSizeInfo coCodeColumns(CompressedSizeInfo colInfos, 
int k) {
-               colInfos.setInfo(join(colInfos.getInfo()));
+
+               List<CompressedSizeInfoColGroup> joinRes = 
join(colInfos.getInfo());
+
+               if(_cs.samplingRatio < 0.1 && _est instanceof 
CompressedSizeEstimatorSample) {
+                       LOG.debug("Performing second join with double sample 
rate");
+                       CompressedSizeEstimatorSample estS = 
(CompressedSizeEstimatorSample) _est;
+                       estS.sampleData(estS.getSample().getNumRows() * 2);
+                       List<int[]> colG = new ArrayList<>(joinRes.size());
+                       for(CompressedSizeInfoColGroup g : joinRes)
+                               colG.add(g.getColumns());
+
+                       joinRes = join(estS.computeCompressedSizeInfos(colG, 
k));
+               }
+
+               colInfos.setInfo(joinRes);
+
                return colInfos;
        }
 
@@ -66,6 +73,8 @@ public class CoCodeCostMatrixMult extends AColumnCoCoder {
                                        final CostOfJoin r = que.poll();
                                        final double costIndividual = (l.cost + 
r.cost);
                                        final CostOfJoin g = new 
CostOfJoin(joinWithAnalysis(l.elm, r.elm));
+                                       if(LOG.isDebugEnabled())
+                                               LOG.debug("\nl:      " + l + 
"\nr:      " + r + "\njoined: " + g);
                                        if(g.cost < costIndividual)
                                                que.add(g);
                                        else {
@@ -81,6 +90,7 @@ public class CoCodeCostMatrixMult extends AColumnCoCoder {
                        else
                                break;
                }
+
                for(CostOfJoin g : que)
                        ret.add(g.elm);
 
@@ -94,30 +104,16 @@ public class CoCodeCostMatrixMult extends AColumnCoCoder {
                protected CostOfJoin(CompressedSizeInfoColGroup elm) {
                        this.elm = elm;
 
-                       final double constantOverheadForColGroup = 5;
-                       final double nCols = elm.getColumns().length;
+                       final int nCols = elm.getColumns().length;
                        final double nRows = _est.getNumRows();
-                       if(elm.getBestCompressionType() == 
CompressionType.UNCOMPRESSED)
-                               this.cost = nRows * nCols * 2 + 
constantOverheadForColGroup;
-                       else {
-                               final int blksz = 
CompressionSettings.BITMAP_BLOCK_SZ;
-
-                               // LOG.error(constantOverheadForColGroup);
-                               final double commonFraction = 
elm.getMostCommonFraction();
-                               final double rowsCost = commonFraction > 0.2 ? 
nRows * (1 - commonFraction) : nRows;
-                               // this.cost = rowsToProcess + elm.getNumVals() 
* nCols + constantOverheadForColGroup;
-                               // this.cost = rowsToProcess + elm.getNumVals() 
* nCols * (1 - commonFraction) +
-                               // constantOverheadForColGroup;
-                               // final double sparsity_tuple_effect = 
elm.getTupleSparsity() > 0.4 ? 1 -
-                               // Math.min(elm.getTupleSparsity(), 0.9) : 1;
-                               final int numberTuples = elm.getNumVals();
-                               final double tuplesCost = (numberTuples < 
blksz) ? numberTuples : numberTuples * 2;
-
-                               // this.cost = elementsCost;
-                               // this.cost = rowsCost + tuplesCost * 
sparsity_tuple_effect + constantOverheadForColGroup;
-
-                               this.cost = rowsCost + tuplesCost + 
constantOverheadForColGroup;
-                       }
+                       final double preAggregateCost = nRows;
+
+                       final int numberTuples = elm.getNumVals();
+                       final double tupleSparsity = elm.getTupleSparsity();
+                       final double postScalingCost = (nCols > 1 && 
elm.getTupleSparsity() > 0.4) ? numberTuples *
+                               nCols : numberTuples * nCols * tupleSparsity;
+
+                       this.cost = preAggregateCost + postScalingCost;
                }
 
                @Override
@@ -128,10 +124,14 @@ public class CoCodeCostMatrixMult extends AColumnCoCoder {
                @Override
                public String toString() {
                        StringBuilder sb = new StringBuilder();
-                       sb.append("\n");
                        sb.append(cost);
                        sb.append(" - ");
+                       sb.append(elm.getBestCompressionType());
+                       sb.append(" nrVals: ");
+                       sb.append(elm.getNumVals());
+                       sb.append(" ");
                        sb.append(Arrays.toString(elm.getColumns()));
+
                        return sb.toString();
                }
        }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeStatic.java 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeStatic.java
index 06e01b4..674a819 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeStatic.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/cocode/CoCodeStatic.java
@@ -29,8 +29,8 @@ import 
org.apache.sysds.runtime.compress.estim.CompressedSizeInfo;
  */
 public class CoCodeStatic extends AColumnCoCoder {
 
-       protected CoCodeStatic(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs, int numRows) {
-               super(sizeEstimator, cs, numRows);
+       protected CoCodeStatic(CompressedSizeEstimator sizeEstimator, 
CompressionSettings cs) {
+               super(sizeEstimator, cs);
        }
 
        @Override
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/PlanningCoCoder.java 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/PlanningCoCoder.java
index 94572c9..3bae0e5 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/cocode/PlanningCoCoder.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/cocode/PlanningCoCoder.java
@@ -67,7 +67,7 @@ public class PlanningCoCoder {
                        List<CompressedSizeInfoColGroup> newGroups = new 
ArrayList<>();
                        mem = new Memorizer();
                        for(CompressedSizeInfoColGroup g : colInfos.getInfo()) {
-                               if(g.getBestCompressionType() == 
CompressionType.CONST)
+                               if(g.getBestCompressionType(cs) == 
CompressionType.CONST)
                                        constantGroups.add(g);
                                else {
                                        mem.put(g);
@@ -93,13 +93,13 @@ public class PlanningCoCoder {
                CompressionSettings cs, int numRows) {
                switch(type) {
                        case BIN_PACKING:
-                               return new CoCodeBinPacking(est, cs, numRows);
+                               return new CoCodeBinPacking(est, cs);
                        case STATIC:
-                               return new CoCodeStatic(est, cs, numRows);
+                               return new CoCodeStatic(est, cs);
                        case COST:
-                               return new CoCodeCost(est, cs, numRows);
+                               return new CoCodeCost(est, cs);
                        case COST_MATRIX_MULT:
-                               return new CoCodeCostMatrixMult(est, cs, 
numRows);
+                               return new CoCodeCostMatrixMult(est, cs);
                        default:
                                throw new RuntimeException("Unsupported column 
group partitioner: " + type.toString());
                }
@@ -186,7 +186,7 @@ public class PlanningCoCoder {
                                break;
                }
 
-               LOG.error(mem.stats());
+               LOG.debug(mem.stats());
                mem.resetStats();
 
                List<CompressedSizeInfoColGroup> ret = new 
ArrayList<>(workset.size());
@@ -226,9 +226,9 @@ public class PlanningCoCoder {
                        if(g == null) {
                                final CompressedSizeInfoColGroup left = 
mem.get(new ColIndexes(c1));
                                final CompressedSizeInfoColGroup right = 
mem.get(new ColIndexes(c2));
-                               final boolean leftConst = 
left.getBestCompressionType() == CompressionType.CONST &&
+                               final boolean leftConst = 
left.getBestCompressionType(cs) == CompressionType.CONST &&
                                        left.getNumOffs() == 0;
-                               final boolean rightConst = 
right.getBestCompressionType() == CompressionType.CONST &&
+                               final boolean rightConst = 
right.getBestCompressionType(cs) == CompressionType.CONST &&
                                        right.getNumOffs() == 0;
                                if(leftConst)
                                        g = 
CompressedSizeInfoColGroup.addConstGroup(c, right, cs.validCompressions);
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/AColGroup.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/AColGroup.java
index ddc6195..6b74136 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/colgroup/AColGroup.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/colgroup/AColGroup.java
@@ -32,6 +32,7 @@ import org.apache.sysds.runtime.matrix.data.MatrixBlock;
 import org.apache.sysds.runtime.matrix.operators.AggregateUnaryOperator;
 import org.apache.sysds.runtime.matrix.operators.BinaryOperator;
 import org.apache.sysds.runtime.matrix.operators.ScalarOperator;
+import org.apache.sysds.utils.MemoryEstimates;
 
 import edu.emory.mathcs.backport.java.util.Arrays;
 
@@ -143,6 +144,15 @@ public abstract class AColGroup implements Serializable {
        public abstract int getNumRows();
 
        /**
+        * Obtain number of distinct tuples in contained sets of values 
associated with this column group.
+        * 
+        * If the column group is uncompressed the number or rows is returned.
+        * 
+        * @return the number of distinct sets of values associated with the 
bitmaps in this column group
+        */
+       public abstract int getNumValues();
+
+       /**
         * Obtain the number of columns in this column group.
         * 
         * @return number of columns in this column group
@@ -183,7 +193,11 @@ public abstract class AColGroup implements Serializable {
         * 
         * @return an upper bound on the number of bytes used to store this 
ColGroup in memory.
         */
-       public abstract long estimateInMemorySize();
+       public long estimateInMemorySize(){
+               long size = 16; // object header
+               size += MemoryEstimates.intArrayCost(_colIndexes.length);
+               return size;
+       }
 
        /**
         * Decompress the contents of this column group into the specified full 
matrix block.
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupCompressed.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupCompressed.java
index c5d29ba..3b598e6 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupCompressed.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupCompressed.java
@@ -58,8 +58,6 @@ public abstract class ColGroupCompressed extends AColGroup {
                _numRows = numRows;
        }
 
-       public abstract int getNumValues();
-
        public abstract double[] getValues();
 
        public abstract void addMinMax(double[] ret);
@@ -147,4 +145,10 @@ public abstract class ColGroupCompressed extends AColGroup 
{
                return _numRows;
        }
 
+       @Override
+       public long estimateInMemorySize() {
+               long size = super.estimateInMemorySize();
+               size += 4;
+               return size;
+       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupConst.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupConst.java
index 8f6299c..e3c2965 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupConst.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupConst.java
@@ -113,11 +113,6 @@ public class ColGroupConst extends ColGroupValue {
        }
 
        @Override
-       public long estimateInMemorySize() {
-               return ColGroupSizes.estimateInMemorySizeCONST(getNumCols(), 
getNumValues(), isLossy());
-       }
-
-       @Override
        public void decompressToBlockSafe(MatrixBlock target, int rl, int ru, 
int offT, double[] values) {
                decompressToBlockUnSafe(target, rl, ru, offT, values);
                target.setNonZeros(_colIndexes.length * target.getNumRows() + 
target.getNonZeros());
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupDDC.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupDDC.java
index df45f56..fa967da 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupDDC.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupDDC.java
@@ -555,8 +555,9 @@ public class ColGroupDDC extends ColGroupValue {
 
        @Override
        public long estimateInMemorySize() {
-               return ColGroupSizes.estimateInMemorySizeDDC(getNumCols(), 
getNumValues(), _numRows, isLossy());
-
+               long size = super.estimateInMemorySize();
+               size += _data.getInMemorySize();
+               return size;
        }
 
        @Override
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupEmpty.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupEmpty.java
index c873b1a..be33491 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupEmpty.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupEmpty.java
@@ -83,10 +83,6 @@ public class ColGroupEmpty extends ColGroupCompressed {
                return ColGroupType.EMPTY;
        }
 
-       @Override
-       public long estimateInMemorySize() {
-               return ColGroupSizes.estimateInMemorySizeEMPTY(getNumCols());
-       }
 
        @Override
        public void decompressToBlockSafe(MatrixBlock target, int rl, int ru, 
int offT, double[] values) {
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupFactory.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupFactory.java
index 62acf71..ffcc2fb 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupFactory.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupFactory.java
@@ -34,9 +34,10 @@ import org.apache.commons.logging.LogFactory;
 import org.apache.sysds.runtime.DMLCompressionException;
 import org.apache.sysds.runtime.DMLRuntimeException;
 import org.apache.sysds.runtime.compress.CompressionSettings;
+import 
org.apache.sysds.runtime.compress.cocode.PlanningCoCoder.PartitionerType;
 import org.apache.sysds.runtime.compress.colgroup.AColGroup.CompressionType;
 import org.apache.sysds.runtime.compress.colgroup.dictionary.ADictionary;
-import org.apache.sysds.runtime.compress.colgroup.dictionary.Dictionary;
+import org.apache.sysds.runtime.compress.colgroup.dictionary.DictionaryFactory;
 import org.apache.sysds.runtime.compress.colgroup.mapping.AMapToData;
 import org.apache.sysds.runtime.compress.colgroup.mapping.MapToFactory;
 import org.apache.sysds.runtime.compress.colgroup.tree.AInsertionSorter;
@@ -47,7 +48,6 @@ import 
org.apache.sysds.runtime.compress.estim.CompressedSizeInfo;
 import org.apache.sysds.runtime.compress.estim.CompressedSizeInfoColGroup;
 import org.apache.sysds.runtime.compress.lib.BitmapEncoder;
 import org.apache.sysds.runtime.compress.utils.ABitmap;
-import org.apache.sysds.runtime.compress.utils.Bitmap;
 import org.apache.sysds.runtime.compress.utils.IntArrayList;
 import org.apache.sysds.runtime.data.SparseBlock;
 import org.apache.sysds.runtime.matrix.data.MatrixBlock;
@@ -155,8 +155,9 @@ public class ColGroupFactory {
 
        private static Collection<AColGroup> compressColGroup(MatrixBlock in, 
int[] colIndexes,
                CompressionSettings compSettings) {
-               if(in.isInSparseFormat() && compSettings.transposed) {
-
+               if(in.isEmpty())
+                       return Collections.singletonList(new 
ColGroupEmpty(colIndexes, compSettings.transposed ? in.getNumColumns(): 
in.getNumRows()));
+               else if(in.isInSparseFormat() && compSettings.transposed) {
                        final SparseBlock sb = in.getSparseBlock();
                        for(int col : colIndexes)
                                if(sb.isEmpty(col))
@@ -191,7 +192,7 @@ public class ColGroupFactory {
 
        private static AColGroup compressColGroupForced(MatrixBlock in, int[] 
colIndexes,
                CompressionSettings compSettings) {
-                       
+
                ABitmap ubm = BitmapEncoder.extractBitmap(colIndexes, in, 
compSettings.transposed);
 
                CompressedSizeEstimator estimator = new 
CompressedSizeEstimatorExact(in, compSettings);
@@ -200,7 +201,8 @@ public class ColGroupFactory {
                        estimator.estimateCompressedColGroupSize(ubm, 
colIndexes), compSettings.validCompressions);
 
                int numRows = compSettings.transposed ? in.getNumColumns() : 
in.getNumRows();
-               return compress(colIndexes, numRows, ubm, 
sizeInfo.getBestCompressionType(), compSettings, in);
+               return compress(colIndexes, numRows, ubm, 
sizeInfo.getBestCompressionType(compSettings), compSettings, in,
+                       sizeInfo.getTupleSparsity());
        }
 
        // private static AColGroup compressColGroupCorrecting(MatrixBlock in,
@@ -275,17 +277,21 @@ public class ColGroupFactory {
         * @param compType       The CompressionType selected
         * @param cs             The compression Settings used for the given 
compression
         * @param rawMatrixBlock The copy of the original input (maybe 
transposed) MatrixBlock
+        * @param tupleSparsity  The sparsity of the ubs entries.
         * @return A Compressed ColGroup
         */
        public static AColGroup compress(int[] colIndexes, int rlen, ABitmap 
ubm, CompressionType compType,
-               CompressionSettings cs, MatrixBlock rawMatrixBlock) {
+               CompressionSettings cs, MatrixBlock rawMatrixBlock, double 
tupleSparsity) {
+
+               if(compType == CompressionType.UNCOMPRESSED && 
cs.columnPartitioner == PartitionerType.COST_MATRIX_MULT)
+                       compType = CompressionType.DDC;
 
                final IntArrayList[] of = ubm.getOffsetList();
 
                if(of == null)
                        return new ColGroupEmpty(colIndexes, rlen);
                else if(of.length == 1 && of[0].size() == rlen)
-                       return new ColGroupConst(colIndexes, rlen, 
ADictionary.getDictionary(ubm));
+                       return new ColGroupConst(colIndexes, rlen, 
DictionaryFactory.create(ubm));
 
                if(LOG.isTraceEnabled())
                        LOG.trace("compressing to: " + compType);
@@ -295,13 +301,13 @@ public class ColGroupFactory {
 
                        switch(compType) {
                                case DDC:
-                                       return compressDDC(colIndexes, rlen, 
ubm, cs);
+                                       return compressDDC(colIndexes, rlen, 
ubm, cs, tupleSparsity);
                                case RLE:
-                                       return compressRLE(colIndexes, rlen, 
ubm, cs);
+                                       return compressRLE(colIndexes, rlen, 
ubm, cs, tupleSparsity);
                                case OLE:
-                                       return compressOLE(colIndexes, rlen, 
ubm, cs);
+                                       return compressOLE(colIndexes, rlen, 
ubm, cs, tupleSparsity);
                                case SDC:
-                                       return compressSDC(colIndexes, rlen, 
ubm, cs);
+                                       return compressSDC(colIndexes, rlen, 
ubm, cs, tupleSparsity);
                                case UNCOMPRESSED:
                                        return new 
ColGroupUncompressed(colIndexes, rawMatrixBlock, cs.transposed);
                                default:
@@ -316,7 +322,8 @@ public class ColGroupFactory {
                }
        }
 
-       private static AColGroup compressSDC(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs) {
+       private static AColGroup compressSDC(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs,
+               double tupleSparsity) {
 
                int numZeros = (int) ((long) rlen - (int) ubm.getNumOffsets());
                int largestOffset = 0;
@@ -330,17 +337,17 @@ public class ColGroupFactory {
                        index++;
                }
                AColGroup cg;
-               ADictionary dict = new Dictionary(((Bitmap) ubm).getValues());
+               ADictionary dict = DictionaryFactory.create(ubm, tupleSparsity);
                if(numZeros >= largestOffset && ubm.getOffsetList().length == 1)
                        cg = new ColGroupSDCSingleZeros(colIndexes, rlen, dict, 
ubm.getOffsetList()[0].extractValues(true), null);
                else if(ubm.getOffsetList().length == 1) {// todo
-                       dict = moveFrequentToLastDictionaryEntry(dict, ubm, 
rlen, largestIndex);
+                       dict = 
DictionaryFactory.moveFrequentToLastDictionaryEntry(dict, ubm, rlen, 
largestIndex);
                        cg = setupSingleValueSDCColGroup(colIndexes, rlen, ubm, 
dict);
                }
                else if(numZeros >= largestOffset)
                        cg = setupMultiValueZeroColGroup(colIndexes, ubm, rlen, 
dict);
                else {
-                       dict = moveFrequentToLastDictionaryEntry(dict, ubm, 
rlen, largestIndex);
+                       dict = 
DictionaryFactory.moveFrequentToLastDictionaryEntry(dict, ubm, rlen, 
largestIndex);
                        cg = setupMultiValueColGroup(colIndexes, numZeros, 
largestOffset, ubm, rlen, largestIndex, dict);
                }
                return cg;
@@ -397,62 +404,17 @@ public class ColGroupFactory {
                return new ColGroupSDCSingle(colIndexes, numRows, dict, 
_indexes, null);
        }
 
-       private static ADictionary 
moveFrequentToLastDictionaryEntry(ADictionary dict, ABitmap ubm, int numRows,
-               int largestIndex) {
-               final double[] dictValues = dict.getValues();
-               final int zeros = numRows - (int) ubm.getNumOffsets();
-               final int nCol = ubm.getNumColumns();
-               final int offsetToLargest = largestIndex * nCol;
-
-               if(zeros == 0) {
-                       final double[] swap = new double[nCol];
-                       System.arraycopy(dictValues, offsetToLargest, swap, 0, 
nCol);
-                       for(int i = offsetToLargest; i < dictValues.length - 
nCol; i++) {
-                               dictValues[i] = dictValues[i + nCol];
-                       }
-                       System.arraycopy(swap, 0, dictValues, dictValues.length 
- nCol, nCol);
-                       return dict;
-               }
-
-               final int largestIndexSize = 
ubm.getOffsetsList(largestIndex).size();
-               final double[] newDict = new double[dictValues.length + nCol];
-
-               if(zeros > largestIndexSize)
-                       System.arraycopy(dictValues, 0, newDict, 0, 
dictValues.length);
-               else {
-                       System.arraycopy(dictValues, 0, newDict, 0, 
offsetToLargest);
-                       System.arraycopy(dictValues, offsetToLargest + nCol, 
newDict, offsetToLargest,
-                               dictValues.length - offsetToLargest - nCol);
-                       System.arraycopy(dictValues, offsetToLargest, newDict, 
newDict.length - nCol, nCol);
-               }
-               return new Dictionary(newDict);
-       }
-
-       private static AColGroup compressDDC(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs) {
+       private static AColGroup compressDDC(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs,
+               double tupleSparsity) {
 
                boolean _zeros = ubm.getNumOffsets() < (long) rlen;
-               ADictionary dict = ADictionary.getDictionary(ubm);
-               double[] values = dict.getValues();
-               if(_zeros) {
-                       double[] appendedZero = new double[values.length + 
colIndexes.length];
-                       System.arraycopy(values, 0, appendedZero, 0, 
values.length);
-                       dict = new Dictionary(appendedZero);
-               }
-               else
-                       dict = new Dictionary(values);
-
+               ADictionary dict = (_zeros) ? 
DictionaryFactory.createWithAppendedZeroTuple(ubm,
+                       tupleSparsity) : DictionaryFactory.create(ubm, 
tupleSparsity);
                int numVals = ubm.getNumValues();
                AMapToData _data = MapToFactory.create(rlen, numVals + (_zeros 
? 1 : 0));
                if(_zeros)
                        _data.fill(numVals);
 
-               // for(int i = 0; i < numVals; i++) {
-               // int[] tmpList = ubm.getOffsetsList(i).extractValues();
-               // int tmpListSize = ubm.getNumOffsets(i);
-               // for(int k = 0; k < tmpListSize; k++)
-               // _data[tmpList[k]] = (char) i;
-               // }
-
                for(int i = 0; i < numVals; i++) {
                        IntArrayList tmpList = ubm.getOffsetsList(i);
                        final int sz = tmpList.size();
@@ -464,9 +426,10 @@ public class ColGroupFactory {
 
        }
 
-       private static AColGroup compressOLE(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs) {
+       private static AColGroup compressOLE(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs,
+               double tupleSparsity) {
 
-               ADictionary dict = ADictionary.getDictionary(ubm);
+               ADictionary dict = DictionaryFactory.create(ubm, tupleSparsity);
                ColGroupOLE ole = new ColGroupOLE(rlen);
 
                final int numVals = ubm.getNumValues();
@@ -485,9 +448,10 @@ public class ColGroupFactory {
                return ole;
        }
 
-       private static AColGroup compressRLE(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs) {
+       private static AColGroup compressRLE(int[] colIndexes, int rlen, 
ABitmap ubm, CompressionSettings cs,
+               double tupleSparsity) {
 
-               ADictionary dict = ADictionary.getDictionary(ubm);
+               ADictionary dict = DictionaryFactory.create(ubm, tupleSparsity);
                ColGroupRLE rle = new ColGroupRLE(rlen);
                // compress the bitmaps
                final int numVals = ubm.getNumValues();
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOLE.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOLE.java
index 2df2878..bb4f325 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOLE.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOLE.java
@@ -329,11 +329,6 @@ public class ColGroupOLE extends ColGroupOffset {
        }
 
        @Override
-       public long estimateInMemorySize() {
-               return ColGroupSizes.estimateInMemorySizeOLE(getNumCols(), 
getNumValues(), _data.length, _numRows, isLossy());
-       }
-
-       @Override
        public AColGroup scalarOperation(ScalarOperator op) {
                double val0 = op.executeScalar(0);
 
@@ -1209,7 +1204,7 @@ public class ColGroupOLE extends ColGroupOffset {
        }
 
        @Override
-       public Dictionary preAggregateThatSDCSingleStructure(ColGroupSDCSingle 
that, Dictionary ret, boolean preModified){
+       public Dictionary preAggregateThatSDCSingleStructure(ColGroupSDCSingle 
that, Dictionary ret, boolean preModified) {
                throw new NotImplementedException();
        }
 
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOffset.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOffset.java
index d33e816..7b7c595 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOffset.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupOffset.java
@@ -27,6 +27,7 @@ import java.util.Arrays;
 import org.apache.sysds.runtime.compress.colgroup.dictionary.ADictionary;
 import org.apache.sysds.runtime.compress.utils.LinearAlgebraUtils;
 import org.apache.sysds.runtime.functionobjects.Builtin;
+import org.apache.sysds.utils.MemoryEstimates;
 
 /**
  * Base class for column groups encoded with various types of bitmap encoding.
@@ -75,11 +76,10 @@ public abstract class ColGroupOffset extends ColGroupValue {
 
        @Override
        public long estimateInMemorySize() {
-               // Could use a ternary operator, but it looks odd with our code 
formatter here.
-
-               return ColGroupSizes.estimateInMemorySizeOffset(getNumCols(), 
getNumValues(), _ptr.length, _data.length,
-                       isLossy());
-
+               long size = super.estimateInMemorySize();
+               size += MemoryEstimates.intArrayCost(_ptr.length);
+               size += MemoryEstimates.charArrayCost(_data.length);
+               return size;
        }
 
        protected final void sumAllValues(double[] b, double[] c) {
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDC.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDC.java
index e449259..d2cebf5 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDC.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDC.java
@@ -330,7 +330,7 @@ public class ColGroupSDC extends ColGroupValue {
 
        @Override
        public long estimateInMemorySize() {
-               long size = 
ColGroupSizes.estimateInMemorySizeGroupValue(_colIndexes.length, 
getNumValues(), isLossy());
+               long size = super.estimateInMemorySize();
                size += _indexes.getInMemorySize();
                size += _data.getInMemorySize();
                return size;
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingle.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingle.java
index 58649c3..1424072 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingle.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingle.java
@@ -314,7 +314,7 @@ public class ColGroupSDCSingle extends ColGroupValue {
 
        @Override
        public long estimateInMemorySize() {
-               long size = 
ColGroupSizes.estimateInMemorySizeGroupValue(_colIndexes.length, 
getNumValues(), isLossy());
+               long size = super.estimateInMemorySize();
                size += _indexes.getInMemorySize();
                return size;
        }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingleZeros.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingleZeros.java
index 94be81c..997c42a 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingleZeros.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCSingleZeros.java
@@ -187,10 +187,18 @@ public class ColGroupSDCSingleZeros extends ColGroupValue 
{
                final double vals = _dict.aggregateTuples(builtin, 
_colIndexes.length)[0];
                final AIterator it = _indexes.getIterator();
                it.skipTo(rl);
-               while(it.hasNext() && it.value() < ru) {
-                       final int idx = it.value();
-                       it.next();
-                       c[idx] = builtin.execute(c[idx], vals);
+               int rix = rl;
+               for(; rix < ru && it.hasNext(); rix++) {
+                       if(it.value() != rix)
+                               c[rix] = builtin.execute(c[rix], 0);
+                       else {
+                               c[rix] = builtin.execute(c[rix], vals);
+                               it.next();
+                       }
+               }
+
+               for(; rix < ru; rix++) {
+                       c[rix] = builtin.execute(c[rix], 0);
                }
        }
 
@@ -260,7 +268,7 @@ public class ColGroupSDCSingleZeros extends ColGroupValue {
 
        @Override
        public long estimateInMemorySize() {
-               long size = 
ColGroupSizes.estimateInMemorySizeGroupValue(_colIndexes.length, 
getNumValues(), isLossy());
+               long size = super.estimateInMemorySize();
                size += _indexes.getInMemorySize();
                return size;
        }
@@ -450,7 +458,7 @@ public class ColGroupSDCSingleZeros extends ColGroupValue {
        }
 
        @Override
-       public Dictionary preAggregateThatSDCSingleStructure(ColGroupSDCSingle 
that, Dictionary ret, boolean preModified){
+       public Dictionary preAggregateThatSDCSingleStructure(ColGroupSDCSingle 
that, Dictionary ret, boolean preModified) {
                throw new NotImplementedException();
        }
 
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCZeros.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCZeros.java
index 23b06a9..77cf6e2 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCZeros.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSDCZeros.java
@@ -198,9 +198,17 @@ public class ColGroupSDCZeros extends ColGroupValue {
                final double[] vals = _dict.aggregateTuples(builtin, 
_colIndexes.length);
                final AIterator it = _indexes.getIterator();
                it.skipTo(rl);
-               while(it.hasNext() && it.value() < ru) {
-                       final int idx = it.value();
-                       c[idx] = builtin.execute(c[idx], 
vals[getIndex(it.getDataIndexAndIncrement())]);
+
+               int rix = rl;
+               for(; rix < ru && it.hasNext(); rix++) {
+                       if(it.value() != rix)
+                               c[rix] = builtin.execute(c[rix], 0);
+                       else
+                               c[rix] = builtin.execute(c[rix], 
vals[_data.getIndex(it.getDataIndexAndIncrement())]);
+               }
+
+               for(; rix < ru; rix++) {
+                       c[rix] = builtin.execute(c[rix], 0);
                }
        }
 
@@ -277,7 +285,7 @@ public class ColGroupSDCZeros extends ColGroupValue {
 
        @Override
        public long estimateInMemorySize() {
-               long size = 
ColGroupSizes.estimateInMemorySizeGroupValue(_colIndexes.length, 
getNumValues(), isLossy());
+               long size = super.estimateInMemorySize();
                size += _indexes.getInMemorySize();
                size += _data.getInMemorySize();
                return size;
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSizes.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSizes.java
index 3c8c50a..faa3bb3 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSizes.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupSizes.java
@@ -32,67 +32,68 @@ public class ColGroupSizes {
        protected static final Log LOG = 
LogFactory.getLog(ColGroupSizes.class.getName());
 
        public static long estimateInMemorySizeGroup(int nrColumns) {
-               long size = 0;
-               size += 16; // Object header
+               long size = 16; // Object header
                size += MemoryEstimates.intArrayCost(nrColumns);
                return size;
        }
 
-       public static long estimateInMemorySizeGroupValue(int nrColumns, int 
nrValues, boolean lossy) {
-               long size = estimateInMemorySizeGroup(nrColumns);
+       public static long estimateInMoemorySizeCompressedColumn(int nrColumns) 
{
+               return estimateInMemorySizeGroup(nrColumns) + 4; // 4 for num 
Rows;
+       }
+
+       public static long estimateInMemorySizeGroupValue(int nrColumns, int 
nrValues, double tupleSparsity,
+               boolean lossy) {
+               long size = estimateInMoemorySizeCompressedColumn(nrColumns);
                // LOG.error("MemorySize Group Value: " + nrColumns + " " + 
nrValues + " " + lossy);
                size += 8; // Dictionary Reference.
                size += 8; // Counts reference
-               size += 4; // int numRows
                size += 1; // _zeros boolean reference
                size += 1; // _lossy boolean reference
                size += 2; // padding
-               size += DictionaryFactory.getInMemorySize(nrValues, nrColumns, 
lossy);
+               size += DictionaryFactory.getInMemorySize(nrValues, nrColumns, 
tupleSparsity, lossy);
                return size;
        }
 
-       public static long estimateInMemorySizeDDC(int nrCols, int numTuples, 
int dataLength, boolean lossy) {
+       public static long estimateInMemorySizeDDC(int nrCols, int numTuples, 
int dataLength, double tupleSparsity,
+               boolean lossy) {
                // LOG.error("Arguments for DDC memory Estimate " + nrCols + " 
" + numTuples + " " + dataLength + " " + lossy);
-               long size = estimateInMemorySizeGroupValue(nrCols, numTuples, 
lossy);
-               size += 8; // Map toFactory reference;
+               long size = estimateInMemorySizeGroupValue(nrCols, numTuples, 
tupleSparsity, lossy);
                size += MapToFactory.estimateInMemorySize(dataLength, 
numTuples);
                return size;
        }
 
        public static long estimateInMemorySizeOffset(int nrColumns, int 
nrValues, int pointers, int offsetLength,
-               boolean lossy) {
+               double tupleSparsity, boolean lossy) {
                // LOG.error("Offset Size: " + nrColumns + " " + nrValues + " " 
+ pointers + " " + offsetLength);
-               long size = estimateInMemorySizeGroupValue(nrColumns, nrValues, 
lossy);
+               long size = estimateInMemorySizeGroupValue(nrColumns, nrValues, 
tupleSparsity, lossy);
                size += MemoryEstimates.intArrayCost(pointers);
                size += MemoryEstimates.charArrayCost(offsetLength);
                return size;
        }
 
        public static long estimateInMemorySizeOLE(int nrColumns, int nrValues, 
int offsetLength, int nrRows,
-               boolean lossy) {
+               double tupleSparsity, boolean lossy) {
                // LOG.error(nrColumns + " " + nrValues + " " + offsetLength + 
" " + nrRows + " " + lossy);
                nrColumns = nrColumns > 0 ? nrColumns : 1;
                offsetLength += (nrRows / CompressionSettings.BITMAP_BLOCK_SZ) 
* 2;
-               long size = 0;
-               size = estimateInMemorySizeOffset(nrColumns, nrValues, 
(nrValues / nrColumns) + 1, offsetLength, lossy);
-               if(nrRows > CompressionSettings.BITMAP_BLOCK_SZ * 2) {
-                       size += MemoryEstimates.intArrayCost((int) nrValues / 
nrColumns);
-               }
+               long size = estimateInMemorySizeOffset(nrColumns, nrValues, 
nrValues  + 1, offsetLength,
+                       tupleSparsity, lossy);
                return size;
        }
 
-       public static long estimateInMemorySizeRLE(int nrColumns, int nrValues, 
int nrRuns, int nrRows, boolean lossy) {
+       public static long estimateInMemorySizeRLE(int nrColumns, int nrValues, 
int nrRuns, int nrRows,
+               double tupleSparsity, boolean lossy) {
                // LOG.error("RLE Size: " + nrColumns + " " + nrValues + " " + 
nrRuns + " " + nrRows);
                int offsetLength = (nrRuns) * 2;
-               long size = estimateInMemorySizeOffset(nrColumns, nrValues, 
(nrValues) + 1, offsetLength, lossy);
+               long size = estimateInMemorySizeOffset(nrColumns, nrValues, 
(nrValues) + 1, offsetLength, tupleSparsity, lossy);
 
                return size;
        }
 
        public static long estimateInMemorySizeSDC(int nrColumns, int nrValues, 
int nrRows, int largestOff,
-               boolean largestOffIsZero, boolean containNoZeroValues, boolean 
lossy) {
+               boolean largestOffIsZero, boolean containNoZeroValues, double 
tupleSparsity, boolean lossy) {
                long size = estimateInMemorySizeGroupValue(nrColumns,
-                       nrValues + (largestOffIsZero || containNoZeroValues ? 0 
: 1), lossy);
+                       nrValues + (largestOffIsZero || containNoZeroValues ? 0 
: 1), tupleSparsity, lossy);
                // LOG.error("SDC Estimation values: " + nrColumns + " " + 
nrValues + " " + nrRows + " " + largestOff);
                size += OffsetFactory.estimateInMemorySize(nrRows - largestOff 
- 1, nrRows);
                if(nrValues > 1)
@@ -101,22 +102,20 @@ public class ColGroupSizes {
        }
 
        public static long estimateInMemorySizeSDCSingle(int nrColumns, int 
nrValues, int nrRows, int largestOff,
-               boolean largestOffIsZero, boolean containNoZeroValues, boolean 
lossy) {
+               boolean largestOffIsZero, boolean containNoZeroValues, double 
tupleSparsity, boolean lossy) {
                long size = estimateInMemorySizeGroupValue(nrColumns,
-                       nrValues + (largestOffIsZero || containNoZeroValues ? 0 
: 1), lossy);
+                       nrValues + (largestOffIsZero || containNoZeroValues ? 0 
: 1), tupleSparsity, lossy);
                size += OffsetFactory.estimateInMemorySize(nrRows - largestOff, 
nrRows);
                return size;
        }
 
-       public static long estimateInMemorySizeCONST(int nrColumns, int 
nrValues, boolean lossy) {
-               long size = estimateInMemorySizeGroupValue(nrColumns, nrValues, 
lossy);
+       public static long estimateInMemorySizeCONST(int nrColumns, int 
nrValues, double tupleSparsity, boolean lossy) {
+               long size = estimateInMemorySizeGroupValue(nrColumns, nrValues, 
tupleSparsity, lossy);
                return size;
        }
 
        public static long estimateInMemorySizeEMPTY(int nrColumns) {
-               long size = estimateInMemorySizeGroup(nrColumns);
-               size += 8; // null pointer to _dict
-               return size;
+               return estimateInMoemorySizeCompressedColumn(nrColumns);
        }
 
        public static long estimateInMemorySizeUncompressed(int nrRows, int 
nrColumns, double sparsity) {
@@ -124,7 +123,7 @@ public class ColGroupSizes {
                // Since the Object is a col group the overhead from the Memory 
Size group is added
                size += estimateInMemorySizeGroup(nrColumns);
                size += 8; // reference to MatrixBlock.
-               size += MatrixBlock.estimateSizeInMemory(nrRows, nrColumns, 
(nrColumns > 1) ?  sparsity : 1);
+               size += MatrixBlock.estimateSizeInMemory(nrRows, nrColumns, 
(nrColumns > 1) ? sparsity : 1);
                return size;
        }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupUncompressed.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupUncompressed.java
index 3cec6fb..c8f9bf6 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupUncompressed.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupUncompressed.java
@@ -660,4 +660,9 @@ public class ColGroupUncompressed extends AColGroup {
                LibMatrixMult.matrixMult(_data, right, out, 
InfrastructureAnalyzer.getLocalParallelism());
                return new ColGroupUncompressed(outputCols, out, false);
        }
+
+       @Override
+       public int getNumValues() {
+               return _data.getNumRows();
+       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupValue.java 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupValue.java
index fc7da24..a0c127a 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupValue.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/ColGroupValue.java
@@ -33,6 +33,7 @@ import org.apache.sysds.runtime.DMLCompressionException;
 import org.apache.sysds.runtime.compress.colgroup.dictionary.ADictionary;
 import org.apache.sysds.runtime.compress.colgroup.dictionary.Dictionary;
 import org.apache.sysds.runtime.compress.colgroup.dictionary.DictionaryFactory;
+import 
org.apache.sysds.runtime.compress.colgroup.dictionary.MatrixBlockDictionary;
 import org.apache.sysds.runtime.compress.colgroup.pre.ArrPreAggregate;
 import org.apache.sysds.runtime.compress.colgroup.pre.IPreAggregate;
 import 
org.apache.sysds.runtime.controlprogram.parfor.stat.InfrastructureAnalyzer;
@@ -93,11 +94,7 @@ public abstract class ColGroupValue extends 
ColGroupCompressed implements Clonea
                decompressToBlock(target, rl, ru, offT, getValues());
        }
 
-       /**
-        * Obtain number of distinct sets of values associated with the bitmaps 
in this column group.
-        * 
-        * @return the number of distinct sets of values associated with the 
bitmaps in this column group
-        */
+       @Override
        public final int getNumValues() {
                return _dict.getNumberOfValues(_colIndexes.length);
        }
@@ -250,22 +247,21 @@ public abstract class ColGroupValue extends 
ColGroupCompressed implements Clonea
                return aggregateColumns;
        }
 
-       private Pair<int[], double[]> preaggValuesFromDense(final int numVals, 
final double[] b, double[] dictVals,
-               final int cl, final int cu, final int cut) {
+       private Pair<int[], double[]> preaggValuesFromDense(final int numVals, 
final double[] b, final int cl, final int cu,
+               final int cut) {
 
-               int[] aggregateColumns = getAggregateColumnsSetDense(b, cl, cu, 
cut);
-               double[] ret = new double[numVals * aggregateColumns.length];
+               final int[] aggregateColumns = getAggregateColumnsSetDense(b, 
cl, cu, cut);
+               final double[] ret = new double[numVals * 
aggregateColumns.length];
 
                for(int k = 0, off = 0;
                        k < numVals * _colIndexes.length;
                        k += _colIndexes.length, off += 
aggregateColumns.length) {
                        for(int h = 0; h < _colIndexes.length; h++) {
                                int idb = _colIndexes[h] * cut;
-                               double v = dictVals[k + h];
-                               for(int i = 0; i < aggregateColumns.length; 
i++) {
-                                       ret[off + i] += v * b[idb + 
aggregateColumns[i]];
-                               }
-
+                               double v = _dict.getValue(k + h);
+                               if(v != 0)
+                                       for(int i = 0; i < 
aggregateColumns.length; i++)
+                                               ret[off + i] += v * b[idb + 
aggregateColumns[i]];
                        }
                }
 
@@ -290,8 +286,7 @@ public abstract class ColGroupValue extends 
ColGroupCompressed implements Clonea
                return aggregateColumns;
        }
 
-       private Pair<int[], double[]> preaggValuesFromSparse(int numVals, 
SparseBlock b, double[] dictVals, int cl, int cu,
-               int cut) {
+       private Pair<int[], double[]> preaggValuesFromSparse(int numVals, 
SparseBlock b, int cl, int cu, int cut) {
 
                int[] aggregateColumns = getAggregateColumnsSetSparse(b);
 
@@ -310,7 +305,7 @@ public abstract class ColGroupValue extends 
ColGroupCompressed implements Clonea
                                                for(int j = 0, offOrg = h;
                                                        j < numVals * 
aggregateColumns.length;
                                                        j += 
aggregateColumns.length, offOrg += _colIndexes.length) {
-                                                       ret[j + retIdx] += 
dictVals[offOrg] * sValues[i];
+                                                       ret[j + retIdx] += 
_dict.getValue(offOrg) * sValues[i];
                                                }
                                }
                        }
@@ -318,18 +313,18 @@ public abstract class ColGroupValue extends 
ColGroupCompressed implements Clonea
                return new ImmutablePair<>(aggregateColumns, ret);
        }
 
-       public Pair<int[], double[]> preaggValues(int numVals, MatrixBlock b, 
double[] dictVals, int cl, int cu, int cut) {
-               return b.isInSparseFormat() ? preaggValuesFromSparse(numVals, 
b.getSparseBlock(), dictVals, cl, cu,
-                       cut) : preaggValuesFromDense(numVals, 
b.getDenseBlockValues(), dictVals, cl, cu, cut);
+       public Pair<int[], double[]> preaggForRightMultiplyValues(int numVals, 
MatrixBlock b, int cl, int cu, int cut) {
+               return b.isInSparseFormat() ? preaggValuesFromSparse(numVals, 
b.getSparseBlock(), cl, cu,
+                       cut) : preaggValuesFromDense(numVals, 
b.getDenseBlockValues(), cl, cu, cut);
        }
 
-       protected static double[] sparsePreaggValues(int numVals, double v, 
boolean allocNew, double[] dictVals) {
-               double[] ret = allocNew ? new double[numVals + 1] : 
allocDVector(numVals + 1, true);
+       // protected static double[] sparsePreaggValues(int numVals, double v, 
boolean allocNew, ADictionary dict) {
+       // double[] ret = allocNew ? new double[numVals + 1] : 
allocDVector(numVals + 1, true);
 
-               for(int k = 0; k < numVals; k++)
-                       ret[k] = dictVals[k] * v;
-               return ret;
-       }
+       // for(int k = 0; k < numVals; k++)
+       // ret[k] = dictVals[k] * v;
+       // return ret;
+       // }
 
        protected double computeMxx(double c, Builtin builtin) {
                if(_zeros)
@@ -1016,9 +1011,10 @@ public abstract class ColGroupValue extends 
ColGroupCompressed implements Clonea
         */
        public void leftMultByMatrix(MatrixBlock matrix, MatrixBlock result, 
double[] values, int rl, int ru) {
                final int numVals = getNumValues();
+               if(!(_dict instanceof MatrixBlockDictionary))
+                       _dict = 
_dict.getAsMatrixBlockDictionary(_colIndexes.length);
 
-               DenseBlock dictV = new DenseBlockFP64(new int[] {numVals, 
_colIndexes.length}, values);
-               MatrixBlock dictM = new MatrixBlock(numVals, 
_colIndexes.length, dictV);
+               MatrixBlock dictM = ((MatrixBlockDictionary) 
_dict).getMatrixBlock();
                dictM.examSparsity();
                MatrixBlock tmpRes = new MatrixBlock(1, _colIndexes.length, 
false);
                for(int i = rl; i < ru; i++) {
@@ -1064,10 +1060,22 @@ public abstract class ColGroupValue extends 
ColGroupCompressed implements Clonea
        }
 
        public AColGroup rightMultByMatrix(MatrixBlock right) {
-               Pair<int[], double[]> pre = preaggValues(getNumValues(), right, 
getValues(), 0, right.getNumColumns(),
+               Pair<int[], double[]> pre = 
preaggForRightMultiplyValues(getNumValues(), right, 0, right.getNumColumns(),
                        right.getNumColumns());
                if(pre.getLeft().length > 0)
                        return copyAndSet(pre.getLeft(), pre.getRight());
                return null;
        }
+
+       @Override
+       public long estimateInMemorySize() {
+               long size = super.estimateInMemorySize();
+               size += 8; // Dictionary Reference.
+               size += 8; // Counts reference
+               size += 1; // _zeros boolean reference
+               size += 1; // _lossy boolean reference
+               size += 2; // padding
+               size += _dict.getInMemorySize();
+               return size;
+       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/ADictionary.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/ADictionary.java
index 352e96b..e5d2a15 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/ADictionary.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/ADictionary.java
@@ -24,9 +24,6 @@ import java.io.IOException;
 
 import org.apache.commons.logging.Log;
 import org.apache.commons.logging.LogFactory;
-import org.apache.sysds.runtime.compress.utils.ABitmap;
-import org.apache.sysds.runtime.compress.utils.Bitmap;
-import org.apache.sysds.runtime.compress.utils.BitmapLossy;
 import org.apache.sysds.runtime.functionobjects.Builtin;
 import org.apache.sysds.runtime.functionobjects.ValueFunction;
 import org.apache.sysds.runtime.matrix.operators.ScalarOperator;
@@ -143,13 +140,7 @@ public abstract class ADictionary {
         * @param fn         The function to apply to individual columns
         * @param colIndexes The mapping to the target columns from the 
individual columns
         */
-       public void aggregateCols(double[] c, Builtin fn, int[] colIndexes) {
-               int ncol = colIndexes.length;
-               int vlen = size() / ncol;
-               for(int k = 0; k < vlen; k++)
-                       for(int j = 0, valOff = k * ncol; j < ncol; j++)
-                               c[colIndexes[j]] = fn.execute(c[colIndexes[j]], 
getValue(valOff + j));
-       }
+       public abstract void aggregateCols(double[] c, Builtin fn, int[] 
colIndexes);
 
        /**
         * Write the dictionary to a DataOutput.
@@ -178,7 +169,7 @@ public abstract class ADictionary {
        public abstract boolean isLossy();
 
        /**
-        * Get the number of values given that the column group has n columns
+        * Get the number of distinct tuples given that the column group has n 
columns
         * 
         * @param ncol The number of Columns in the ColumnGroup.
         * @return the number of value tuples contained in the dictionary.
@@ -254,6 +245,14 @@ public abstract class ADictionary {
 
        public abstract boolean containsValue(double pattern);
 
+       /**
+        * Calculate the number of non zeros in the dictionary. The number of 
non zeros should be scaled with the counts
+        * given
+        * 
+        * @param counts The counts of each dictionary entry
+        * @param nCol   The number of columns in this dictionary
+        * @return The nonZero count
+        */
        public abstract long getNumberNonZeros(int[] counts, int nCol);
 
        public abstract long getNumberNonZerosContained();
@@ -268,13 +267,6 @@ public abstract class ADictionary {
         */
        public abstract void addToEntry(Dictionary d, int fr, int to, int nCol);
 
-       public static ADictionary getDictionary(ABitmap ubm) {
-               if(ubm instanceof BitmapLossy)
-                       return new QDictionary((BitmapLossy) 
ubm).makeDoubleDictionary();
-               else
-                       return new Dictionary(((Bitmap) ubm).getValues());
-       }
-
        /**
         * Get the most common tuple element contained in the dictionary
         * 
@@ -293,4 +285,12 @@ public abstract class ADictionary {
         * @return a new instance of dictionary with the tuple subtracted.
         */
        public abstract ADictionary subtractTuple(double[] tuple);
+
+       /**
+        * Get this dictionary as a matrixBlock dictionary. This allows us to 
use optimized kernels coded elsewhere in the
+        * system, such as matrix multiplication.
+        * 
+        * @return A Dictionary containing a MatrixBlock.
+        */
+       public abstract MatrixBlockDictionary getAsMatrixBlockDictionary(int 
nCol);
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/Dictionary.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/Dictionary.java
index 5a32823..595c250 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/Dictionary.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/Dictionary.java
@@ -25,8 +25,11 @@ import java.io.IOException;
 import java.util.Arrays;
 
 import org.apache.sysds.runtime.DMLCompressionException;
+import org.apache.sysds.runtime.data.DenseBlock;
+import org.apache.sysds.runtime.data.DenseBlockFP64;
 import org.apache.sysds.runtime.functionobjects.Builtin;
 import org.apache.sysds.runtime.functionobjects.ValueFunction;
+import org.apache.sysds.runtime.matrix.data.MatrixBlock;
 import org.apache.sysds.runtime.matrix.operators.ScalarOperator;
 import org.apache.sysds.utils.MemoryEstimates;
 
@@ -473,4 +476,23 @@ public class Dictionary extends ADictionary {
                }
                return new Dictionary(newValues);
        }
+
+       @Override
+       public MatrixBlockDictionary getAsMatrixBlockDictionary(int nCol) {
+               final int nRow = _values.length / nCol;
+               DenseBlock dictV = new DenseBlockFP64(new int[] {nRow, nCol}, 
_values);
+               MatrixBlock dictM = new MatrixBlock(nRow, nCol, dictV);
+               dictM.examSparsity();
+               return new MatrixBlockDictionary(dictM);
+       }
+
+       @Override
+       public void aggregateCols(double[] c, Builtin fn, int[] colIndexes) {
+               int ncol = colIndexes.length;
+               int vlen = size() / ncol;
+               for(int k = 0; k < vlen; k++)
+                       for(int j = 0, valOff = k * ncol; j < ncol; j++)
+                               c[colIndexes[j]] = fn.execute(c[colIndexes[j]], 
getValue(valOff + j));
+               
+       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/DictionaryFactory.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/DictionaryFactory.java
index 328e145..bab32b0 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/DictionaryFactory.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/DictionaryFactory.java
@@ -22,8 +22,20 @@ package 
org.apache.sysds.runtime.compress.colgroup.dictionary;
 import java.io.DataInput;
 import java.io.IOException;
 
+import org.apache.commons.lang.NotImplementedException;
+import org.apache.commons.logging.Log;
+import org.apache.commons.logging.LogFactory;
+import org.apache.sysds.runtime.compress.utils.ABitmap;
+import org.apache.sysds.runtime.compress.utils.Bitmap;
+import org.apache.sysds.runtime.compress.utils.BitmapLossy;
+import org.apache.sysds.runtime.compress.utils.MultiColBitmap;
+import org.apache.sysds.runtime.data.SparseBlock;
+import org.apache.sysds.runtime.matrix.data.MatrixBlock;
+
 public class DictionaryFactory {
 
+       protected static final Log LOG = 
LogFactory.getLog(DictionaryFactory.class.getName());
+
        public static ADictionary read(DataInput in) throws IOException {
                boolean lossy = in.readBoolean();
                if(lossy) {
@@ -46,10 +58,131 @@ public class DictionaryFactory {
                }
        }
 
-       public static long getInMemorySize(int nrValues, int nrColumns, boolean 
lossy) {
+       public static long getInMemorySize(int nrValues, int nrColumns, double 
tupleSparsity, boolean lossy) {
                if(lossy)
                        return QDictionary.getInMemorySize(nrValues * 
nrColumns);
+               else if(nrColumns > 1 && tupleSparsity < 0.4)
+                       return MatrixBlockDictionary.getInMemorySize(nrValues, 
nrColumns, tupleSparsity);
                else
                        return Dictionary.getInMemorySize(nrValues * nrColumns);
        }
+
+       public static ADictionary create(ABitmap ubm) {
+               return create(ubm, 1.0);
+       }
+
+       public static ADictionary create(ABitmap ubm, double sparsity) {
+               if(ubm instanceof BitmapLossy)
+                       return new QDictionary((BitmapLossy) ubm);
+               else if(ubm instanceof Bitmap)
+                       return new Dictionary(((Bitmap) ubm).getValues());
+               else if(sparsity < 0.4 && ubm instanceof MultiColBitmap) {
+                       final int nCols = ubm.getNumColumns();
+                       final int nRows = ubm.getNumValues();
+                       final MultiColBitmap mcbm = (MultiColBitmap) ubm;
+
+                       final MatrixBlock m = new MatrixBlock(nRows, nCols, 
true);
+                       m.allocateSparseRowsBlock();
+                       final SparseBlock sb = m.getSparseBlock();
+
+                       final int nVals = ubm.getNumValues();
+                       for(int i = 0; i < nVals; i++) {
+                               final double[] tuple = mcbm.getValues(i);
+                               for(int col = 0; col < nCols; col++)
+                                       sb.append(i, col, tuple[col]);
+                       }
+                       m.recomputeNonZeros();
+                       return new MatrixBlockDictionary(m);
+               }
+               else if(ubm instanceof MultiColBitmap) {
+                       MultiColBitmap mcbm = (MultiColBitmap) ubm;
+                       final int nCol = ubm.getNumColumns();
+                       final int nVals = ubm.getNumValues();
+                       double[] resValues = new double[nVals * nCol];
+                       for(int i = 0; i < nVals; i++)
+                               System.arraycopy(mcbm.getValues(i), 0, 
resValues, i * nCol, nCol);
+
+                       return new Dictionary(resValues);
+               }
+               throw new NotImplementedException(
+                       "Not implemented creation of bitmap type : " + 
ubm.getClass().getSimpleName());
+       }
+
+       public static ADictionary createWithAppendedZeroTuple(ABitmap ubm) {
+               return createWithAppendedZeroTuple(ubm, 1.0);
+       }
+
+       public static ADictionary createWithAppendedZeroTuple(ABitmap ubm, 
double sparsity) {
+               // Log.warn("Inefficient creation of dictionary, to then 
allocate again.");
+               final int nRows = ubm.getNumValues() + 1;
+               final int nCols = ubm.getNumColumns();
+               if(ubm instanceof Bitmap) {
+                       Bitmap bm = (Bitmap) ubm;
+                       double[] resValues = new double[ubm.getNumValues() + 1];
+                       double[] from = bm.getValues();
+                       System.arraycopy(from, 0, resValues, 0, from.length);
+                       return new Dictionary(resValues);
+               }
+               else if(sparsity < 0.4 && ubm instanceof MultiColBitmap) {
+                       final MultiColBitmap mcbm = (MultiColBitmap) ubm;
+                       final MatrixBlock m = new MatrixBlock(nRows, nCols, 
true);
+                       m.allocateSparseRowsBlock();
+                       final SparseBlock sb = m.getSparseBlock();
+
+                       final int nVals = ubm.getNumValues();
+                       for(int i = 0; i < nVals; i++) {
+                               final double[] tuple = mcbm.getValues(i);
+                               for(int col = 0; col < nCols; col++)
+                                       sb.append(i, col, tuple[col]);
+                       }
+                       m.recomputeNonZeros();
+                       return new MatrixBlockDictionary(m);
+               }
+               else if(ubm instanceof MultiColBitmap) {
+                       MultiColBitmap mcbm = (MultiColBitmap) ubm;
+                       final int nVals = ubm.getNumValues();
+                       double[] resValues = new double[nRows * nCols];
+                       for(int i = 0; i < nVals; i++)
+                               System.arraycopy(mcbm.getValues(i), 0, 
resValues, i * nCols, nCols);
+
+                       return new Dictionary(resValues);
+               }
+               else {
+                       throw new NotImplementedException(
+                               "Not implemented creation of bitmap type : " + 
ubm.getClass().getSimpleName());
+               }
+
+       }
+
+       public static ADictionary moveFrequentToLastDictionaryEntry(ADictionary 
dict, ABitmap ubm, int numRows,
+               int largestIndex) {
+               LOG.warn("Inefficient creation of dictionary, to then allocate 
again to move one entry to end.");
+               final double[] dictValues = dict.getValues();
+               final int zeros = numRows - (int) ubm.getNumOffsets();
+               final int nCol = ubm.getNumColumns();
+               final int offsetToLargest = largestIndex * nCol;
+
+               if(zeros == 0) {
+                       final double[] swap = new double[nCol];
+                       System.arraycopy(dictValues, offsetToLargest, swap, 0, 
nCol);
+                       for(int i = offsetToLargest; i < dictValues.length - 
nCol; i++) {
+                               dictValues[i] = dictValues[i + nCol];
+                       }
+                       System.arraycopy(swap, 0, dictValues, dictValues.length 
- nCol, nCol);
+                       return dict;
+               }
+
+               final int largestIndexSize = 
ubm.getOffsetsList(largestIndex).size();
+               final double[] newDict = new double[dictValues.length + nCol];
+
+               if(zeros > largestIndexSize)
+                       System.arraycopy(dictValues, 0, newDict, 0, 
dictValues.length);
+               else {
+                       System.arraycopy(dictValues, 0, newDict, 0, 
offsetToLargest);
+                       System.arraycopy(dictValues, offsetToLargest + nCol, 
newDict, offsetToLargest,
+                               dictValues.length - offsetToLargest - nCol);
+                       System.arraycopy(dictValues, offsetToLargest, newDict, 
newDict.length - nCol, nCol);
+               }
+               return new Dictionary(newDict);
+       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/MatrixBlockDictionary.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/MatrixBlockDictionary.java
new file mode 100644
index 0000000..322e56b
--- /dev/null
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/MatrixBlockDictionary.java
@@ -0,0 +1,456 @@
+package org.apache.sysds.runtime.compress.colgroup.dictionary;
+
+import org.apache.commons.lang.NotImplementedException;
+import org.apache.sysds.runtime.data.SparseBlock;
+import org.apache.sysds.runtime.functionobjects.Builtin;
+import org.apache.sysds.runtime.functionobjects.Builtin.BuiltinCode;
+import org.apache.sysds.runtime.functionobjects.ValueFunction;
+import org.apache.sysds.runtime.matrix.data.LibMatrixReorg;
+import org.apache.sysds.runtime.matrix.data.MatrixBlock;
+import org.apache.sysds.runtime.matrix.operators.ScalarOperator;
+
+public class MatrixBlockDictionary extends ADictionary {
+
+    private MatrixBlock _data;
+
+    public MatrixBlockDictionary(MatrixBlock data) {
+        _data = data;
+    }
+
+    public MatrixBlock getMatrixBlock() {
+        return _data;
+    }
+
+    @Override
+    public double[] getValues() {
+        LOG.warn("Inefficient force dense format.");
+        _data.sparseToDense();
+        return _data.getDenseBlockValues();
+    }
+
+    @Override
+    public double getValue(int i) {
+        final int nCol = _data.getNumColumns();
+        LOG.warn("inefficient get value at index");
+        return _data.quickGetValue(i / nCol, i % nCol);
+    }
+
+    @Override
+    public int hasZeroTuple(int nCol) {
+        if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                if(sb.isEmpty(i)) {
+                    return i;
+                }
+            }
+        }
+        else {
+            throw new NotImplementedException();
+        }
+        return -1;
+    }
+
+    @Override
+    public long getInMemorySize() {
+        return 8 + _data.estimateSizeInMemory();
+    }
+
+    public static long getInMemorySize(int numberValues, int numberColumns, 
double sparsity) {
+        return 8 + MatrixBlock.estimateSizeInMemory(numberValues, 
numberColumns, sparsity);
+    }
+
+    @Override
+    public double aggregate(double init, Builtin fn) {
+        if(fn.getBuiltinCode() == BuiltinCode.MAX)
+            return fn.execute(init, _data.max());
+        else if(fn.getBuiltinCode() == BuiltinCode.MIN)
+            return fn.execute(init, _data.min());
+        else
+            throw new NotImplementedException();
+    }
+
+    @Override
+    public double[] aggregateTuples(Builtin fn, int nCol) {
+        double[] ret = new double[_data.getNumRows()];
+        if(_data.isEmpty())
+            return ret;
+        else if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                if(!sb.isEmpty(i)) {
+                    final int apos = sb.pos(i);
+                    final int alen = sb.size(i) + apos;
+                    final double[] avals = sb.values(i);
+                    ret[i] = avals[apos];
+                    for(int j = apos + 1; j < alen; j++)
+                        ret[i] = fn.execute(ret[i], avals[j]);
+
+                    if(sb.size(i) < _data.getNumColumns())
+                        ret[i] = fn.execute(ret[i], 0);
+                }
+                else
+                    ret[i] = fn.execute(ret[i], 0);
+            }
+        }
+        else if(nCol == 1)
+            return _data.getDenseBlockValues();
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int k = 0; k < _data.getNumRows(); k++) {
+                ret[k] = values[off++];
+                for(int j = 1; j < _data.getNumColumns(); j++)
+                    ret[k] = fn.execute(ret[k], values[off++]);
+            }
+        }
+        return ret;
+    }
+
+    @Override
+    public void aggregateCols(double[] c, Builtin fn, int[] colIndexes) {
+        if(_data.isEmpty()) {
+            for(int j = 0; j < colIndexes.length; j++) {
+                final int idx = colIndexes[j];
+                c[idx] = fn.execute(c[idx], 0);
+            }
+        }
+        else if(_data.isInSparseFormat()) {
+            MatrixBlock t = LibMatrixReorg.transposeInPlace(_data, 1);
+            if(!t.isInSparseFormat()) {
+                throw new NotImplementedException();
+            }
+            SparseBlock sbt = t.getSparseBlock();
+
+            for(int i = 0; i < _data.getNumColumns(); i++) {
+                final int idx = colIndexes[i];
+                if(!sbt.isEmpty(i)) {
+                    final int apos = sbt.pos(i);
+                    final int alen = sbt.size(i) + apos;
+                    final double[] avals = sbt.values(i);
+                    for(int j = apos; j < alen; j++)
+                        c[idx] = fn.execute(c[idx], avals[j]);
+                    if(avals.length != _data.getNumRows())
+                        c[idx] = fn.execute(c[idx], 0);
+                }
+                else
+                    c[idx] = fn.execute(c[idx], 0);
+            }
+        }
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int k = 0; k < _data.getNumRows(); k++) {
+                for(int j = 0; j < _data.getNumColumns(); j++) {
+                    final int idx = colIndexes[j];
+                    c[idx] = fn.execute(c[idx], values[off++]);
+                }
+            }
+        }
+    }
+
+    @Override
+    public int size() {
+        return (int) _data.getNonZeros();
+    }
+
+    @Override
+    public ADictionary apply(ScalarOperator op) {
+        MatrixBlock res = _data.scalarOperations(op, new MatrixBlock());
+        return new MatrixBlockDictionary(res);
+    }
+
+    @Override
+    public ADictionary applyScalarOp(ScalarOperator op, double newVal, int 
numCols) {
+        MatrixBlock res = _data.scalarOperations(op, new MatrixBlock());
+        MatrixBlock res2 = res.append(new MatrixBlock(1, 1, newVal), new 
MatrixBlock());
+        return new MatrixBlockDictionary(res2);
+    }
+
+    @Override
+    public ADictionary applyBinaryRowOpLeft(ValueFunction fn, double[] v, 
boolean sparseSafe, int[] colIndexes) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public ADictionary applyBinaryRowOpRight(ValueFunction fn, double[] v, 
boolean sparseSafe, int[] colIndexes) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public ADictionary clone() {
+        MatrixBlock ret = new MatrixBlock();
+        ret.copy(_data);
+        return new MatrixBlockDictionary(ret);
+    }
+
+    @Override
+    public ADictionary cloneAndExtend(int len) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public boolean isLossy() {
+        return false;
+    }
+
+    @Override
+    public int getNumberOfValues(int ncol) {
+        return _data.getNumRows();
+    }
+
+    @Override
+    public double[] sumAllRowsToDouble(boolean square, int nrColumns) {
+        double[] ret = new double[_data.getNumRows()];
+
+        if(_data.isEmpty())
+            return ret;
+        else if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                if(!sb.isEmpty(i)) {
+                    final int apos = sb.pos(i);
+                    final int alen = sb.size(i) + apos;
+                    final double[] avals = sb.values(i);
+                    for(int j = apos; j < alen; j++) {
+                        ret[i] += (square) ? avals[j] * avals[j] : avals[j];
+                    }
+                }
+            }
+        }
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int k = 0; k < _data.getNumRows(); k++) {
+                for(int j = 0; j < _data.getNumColumns(); j++) {
+                    final double v = values[off++];
+                    ret[k] += (square) ? v * v : v;
+                }
+            }
+        }
+        return ret;
+    }
+
+    @Override
+    public double sumRow(int k, boolean square, int nrColumns) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public double[] colSum(int[] counts, int nCol) {
+        if(_data.isEmpty())
+            return null;
+        double[] ret = new double[nCol];
+        if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                if(!sb.isEmpty(i)) {
+                    // double tmpSum = 0;
+                    final int count = counts[i];
+                    final int apos = sb.pos(i);
+                    final int alen = sb.size(i) + apos;
+                    final int[] aix = sb.indexes(i);
+                    final double[] avals = sb.values(i);
+                    for(int j = apos; j < alen; j++) {
+                        ret[aix[j]] += count * avals[j];
+                    }
+                }
+            }
+        }
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int k = 0; k < _data.getNumRows(); k++) {
+                final int countK = counts[k];
+                for(int j = 0; j < _data.getNumColumns(); j++) {
+                    final double v = values[off++];
+                    ret[j] += v * countK;
+                }
+            }
+        }
+        return ret;
+    }
+
+    @Override
+    public void colSum(double[] c, int[] counts, int[] colIndexes, boolean 
square) {
+        if(_data.isEmpty())
+            return;
+        if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                if(!sb.isEmpty(i)) {
+                    // double tmpSum = 0;
+                    final int count = counts[i];
+                    final int apos = sb.pos(i);
+                    final int alen = sb.size(i) + apos;
+                    final int[] aix = sb.indexes(i);
+                    final double[] avals = sb.values(i);
+                    for(int j = apos; j < alen; j++) {
+                        c[colIndexes[aix[j]]] += square ? count * avals[j] * 
avals[j] : count * avals[j];
+                    }
+                }
+            }
+        }
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int k = 0; k < _data.getNumRows(); k++) {
+                final int countK = counts[k];
+                for(int j = 0; j < _data.getNumColumns(); j++) {
+                    final double v = values[off++];
+                    c[colIndexes[j]] += square ? v * v * countK : v * countK;
+                }
+            }
+        }
+    }
+
+    @Override
+    public double sum(int[] counts, int ncol) {
+        double tmpSum = 0;
+        if(_data.isEmpty())
+            return tmpSum;
+        if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                if(!sb.isEmpty(i)) {
+                    final int count = counts[i];
+                    final int apos = sb.pos(i);
+                    final int alen = sb.size(i) + apos;
+                    final double[] avals = sb.values(i);
+                    for(int j = apos; j < alen; j++) {
+                        tmpSum += count * avals[j];
+                    }
+                }
+            }
+        }
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int k = 0; k < _data.getNumRows(); k++) {
+                final int countK = counts[k];
+                for(int j = 0; j < _data.getNumColumns(); j++) {
+                    final double v = values[off++];
+                    tmpSum += v * countK;
+                }
+            }
+        }
+        return tmpSum;
+    }
+
+    @Override
+    public double sumsq(int[] counts, int ncol) {
+        double tmpSum = 0;
+        if(_data.isEmpty())
+            return tmpSum;
+        if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                if(!sb.isEmpty(i)) {
+                    final int count = counts[i];
+                    final int apos = sb.pos(i);
+                    final int alen = sb.size(i) + apos;
+                    final double[] avals = sb.values(i);
+                    for(int j = apos; j < alen; j++) {
+                        tmpSum += count * avals[j] * avals[j];
+                    }
+                }
+            }
+        }
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int k = 0; k < _data.getNumRows(); k++) {
+                final int countK = counts[k];
+                for(int j = 0; j < _data.getNumColumns(); j++) {
+                    final double v = values[off++];
+                    tmpSum += v * v * countK;
+                }
+            }
+        }
+        return tmpSum;
+    }
+
+    @Override
+    public String getString(int colIndexes) {
+        return _data.toString();
+    }
+
+    @Override
+    public void addMaxAndMin(double[] ret, int[] colIndexes) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public ADictionary sliceOutColumnRange(int idxStart, int idxEnd, int 
previousNumberOfColumns) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public ADictionary reExpandColumns(int max) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public boolean containsValue(double pattern) {
+        return _data.containsValue(pattern);
+    }
+
+    @Override
+    public long getNumberNonZeros(int[] counts, int nCol) {
+        if(_data.isEmpty())
+            return 0;
+        long nnz = 0;
+        if(_data.isInSparseFormat()) {
+            SparseBlock sb = _data.getSparseBlock();
+            for(int i = 0; i < _data.getNumRows(); i++)
+                if(sb.isEmpty(i))
+                    nnz += sb.size(i) * counts[i];
+
+        }
+        else {
+            double[] values = _data.getDenseBlockValues();
+            int off = 0;
+            for(int i = 0; i < _data.getNumRows(); i++) {
+                int countThisTuple = 0;
+                for(int j = 0; j < _data.getNumColumns(); j++) {
+                    double v = values[off++];
+                    if(v != 0)
+                        countThisTuple++;
+                }
+                nnz += countThisTuple * counts[i];
+            }
+        }
+        return nnz;
+    }
+
+    @Override
+    public long getNumberNonZerosContained() {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public void addToEntry(Dictionary d, int fr, int to, int nCol) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public double[] getMostCommonTuple(int[] counts, int nCol) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public ADictionary subtractTuple(double[] tuple) {
+        throw new NotImplementedException();
+    }
+
+    @Override
+    public MatrixBlockDictionary getAsMatrixBlockDictionary(int nCol) {
+        // Simply return this.
+        return this;
+    }
+
+    @Override
+    public String toString() {
+        return "MatrixBlock Dictionary :" + _data.toString();
+    }
+}
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/QDictionary.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/QDictionary.java
index 7b01fb5..70836ca 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/QDictionary.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/QDictionary.java
@@ -499,4 +499,14 @@ public class QDictionary extends ADictionary {
        public ADictionary subtractTuple(double[] tuple) {
                throw new NotImplementedException();
        }
+
+       @Override
+       public MatrixBlockDictionary getAsMatrixBlockDictionary(int nCol) {
+               throw new NotImplementedException();
+       }
+
+       @Override
+       public void aggregateCols(double[] c, Builtin fn, int[] colIndexes) {
+               throw new NotImplementedException();    
+       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/SparseDictionary.java
 
b/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/SparseDictionary.java
deleted file mode 100644
index 3a400f3..0000000
--- 
a/src/main/java/org/apache/sysds/runtime/compress/colgroup/dictionary/SparseDictionary.java
+++ /dev/null
@@ -1,218 +0,0 @@
-/*
- * Licensed to the Apache Software Foundation (ASF) under one
- * or more contributor license agreements.  See the NOTICE file
- * distributed with this work for additional information
- * regarding copyright ownership.  The ASF licenses this file
- * to you under the Apache License, Version 2.0 (the
- * "License"); you may not use this file except in compliance
- * with the License.  You may obtain a copy of the License at
- *
- *   http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing,
- * software distributed under the License is distributed on an
- * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
- * KIND, either express or implied.  See the License for the
- * specific language governing permissions and limitations
- * under the License.
- */
-
-package org.apache.sysds.runtime.compress.colgroup.dictionary;
-
-import org.apache.sysds.runtime.functionobjects.Builtin;
-import org.apache.sysds.runtime.functionobjects.ValueFunction;
-import org.apache.sysds.runtime.matrix.operators.ScalarOperator;
-
-/**
- * A sparse dictionary implementation, use if the tuples are sparse.
- */
-public class SparseDictionary extends ADictionary {
-
-       @Override
-       public double[] getValues() {
-               LOG.warn("Inefficient materialization of sparse Dictionary.");
-
-               return null;
-       }
-
-       @Override
-       public double getValue(int i) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public int hasZeroTuple(int nCol) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public long getInMemorySize() {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public double aggregate(double init, Builtin fn) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public double[] aggregateTuples(Builtin fn, int nCol) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public int size() {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public ADictionary apply(ScalarOperator op) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public ADictionary applyScalarOp(ScalarOperator op, double newVal, int 
numCols) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public ADictionary applyBinaryRowOpLeft(ValueFunction fn, double[] v, 
boolean sparseSafe, int[] colIndexes) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public ADictionary applyBinaryRowOpRight(ValueFunction fn, double[] v, 
boolean sparseSafe, int[] colIndexes) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public ADictionary clone() {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public ADictionary cloneAndExtend(int len) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public boolean isLossy() {
-               // TODO Auto-generated method stub
-               return false;
-       }
-
-       @Override
-       public int getNumberOfValues(int ncol) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public double[] sumAllRowsToDouble(boolean square, int nrColumns) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public double sumRow(int k, boolean square, int nrColumns) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public double[] colSum(int[] counts, int nCol) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public void colSum(double[] c, int[] counts, int[] colIndexes, boolean 
square) {
-               // TODO Auto-generated method stub
-
-       }
-
-       @Override
-       public double sum(int[] counts, int ncol) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public double sumsq(int[] counts, int ncol) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public String getString(int colIndexes) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public void addMaxAndMin(double[] ret, int[] colIndexes) {
-               // TODO Auto-generated method stub
-
-       }
-
-       @Override
-       public ADictionary sliceOutColumnRange(int idxStart, int idxEnd, int 
previousNumberOfColumns) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public ADictionary reExpandColumns(int max) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public boolean containsValue(double pattern) {
-               // TODO Auto-generated method stub
-               return false;
-       }
-
-       @Override
-       public long getNumberNonZeros(int[] counts, int nCol) {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public long getNumberNonZerosContained() {
-               // TODO Auto-generated method stub
-               return 0;
-       }
-
-       @Override
-       public void addToEntry(Dictionary d, int fr, int to, int nCol) {
-               // TODO Auto-generated method stub
-
-       }
-
-       @Override
-       public double[] getMostCommonTuple(int[] counts, int nCol) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-       @Override
-       public ADictionary subtractTuple(double[] tuple) {
-               // TODO Auto-generated method stub
-               return null;
-       }
-
-}
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimator.java
 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimator.java
index d4b2a63..f46ee53 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimator.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimator.java
@@ -21,6 +21,7 @@ package org.apache.sysds.runtime.compress.estim;
 
 import java.util.ArrayList;
 import java.util.Arrays;
+import java.util.Collection;
 import java.util.List;
 import java.util.concurrent.Callable;
 import java.util.concurrent.ExecutionException;
@@ -91,6 +92,52 @@ public abstract class CompressedSizeEstimator {
                return new CompressedSizeInfo(sizeInfos);
        }
 
+       /**
+        * Multi threaded version of extracting Compression Size info from list 
of specified columns
+        * 
+        * @return
+        */
+
+       /**
+        * Multi threaded version of extracting Compression Size info from list 
of specified columns
+        * 
+        * @param columnLists The specified columns to extract.
+        * @param k           The parallelization degree
+        * @return The Compression information from the specified column groups.
+        */
+       public List<CompressedSizeInfoColGroup> 
computeCompressedSizeInfos(Collection<int[]> columnLists, int k) {
+               if(k == 1)
+                       return computeCompressedSizeInfos(columnLists);
+               try {
+                       ExecutorService pool = CommonThreadPool.get(k);
+                       ArrayList<SizeEstimationTask> tasks = new ArrayList<>();
+                       for(int[] g : columnLists)
+                               tasks.add(new SizeEstimationTask(this, g));
+                       List<Future<CompressedSizeInfoColGroup>> rtask = 
pool.invokeAll(tasks);
+                       ArrayList<CompressedSizeInfoColGroup> ret = new 
ArrayList<>();
+                       for(Future<CompressedSizeInfoColGroup> lrtask : rtask)
+                               ret.add(lrtask.get());
+                       pool.shutdown();
+                       return ret;
+               }
+               catch(InterruptedException | ExecutionException e) {
+                       return computeCompressedSizeInfos(columnLists);
+               }
+       }
+
+       /**
+        * Compression Size info from list of specified columns
+        * 
+        * @param columnLists The specified columns to extract.
+        * @return The Compression information from the specified column groups.
+        */
+       public List<CompressedSizeInfoColGroup> 
computeCompressedSizeInfos(Collection<int[]> columnLists) {
+               ArrayList<CompressedSizeInfoColGroup> ret = new ArrayList<>();
+               for(int[] g : columnLists)
+                       ret.add(estimateCompressedColGroupSize(g));
+               return ret;
+       }
+
        private CompressedSizeInfoColGroup[] 
estimateIndividualColumnGroupSizes(int k) {
                return (k > 1) ? CompressedSizeInfoColGroup(_numCols, k) : 
CompressedSizeInfoColGroup(_numCols);
        }
@@ -106,19 +153,36 @@ public abstract class CompressedSizeEstimator {
        }
 
        /**
-        * Abstract method for extracting Compressed Size Info of specified 
columns, together in a single ColGroup
+        * Method for extracting Compressed Size Info of specified columns, 
together in a single ColGroup
         * 
-        * @param colIndexes The Colums to group together inside a ColGroup
+        * @param colIndexes The columns to group together inside a ColGroup
         * @return The CompressedSizeInformation associated with the selected 
ColGroups.
         */
-       public abstract CompressedSizeInfoColGroup 
estimateCompressedColGroupSize(int[] colIndexes);
+       public CompressedSizeInfoColGroup estimateCompressedColGroupSize(int[] 
colIndexes) {
+               return estimateCompressedColGroupSize(colIndexes, 
Integer.MAX_VALUE);
+       }
+
+       /**
+        * A method to extract the Compressed Size Info for a given list of 
columns, This method further limits the
+        * estimated number of unique values, since in some cases the estimated 
number of uniques is estimated higher than
+        * the number estimated in sub groups of the given colIndexes.
+        * 
+        * @param colIndexes         The columns to extract compression 
information from
+        * @param nrUniqueUpperBound The upper bound of unique elements allowed 
in the estimate, can be calculated from the
+        *                           number of unique elements estimated in sub 
columns multiplied together. This is
+        *                           flexible in the sense that if the sample 
is small then this unique can be manually
+        *                           edited like in CoCodeCostMatrixMult.
+        * 
+        * @return The CompressedSizeInfoColGroup fro the given column indexes.
+        */
+       public abstract CompressedSizeInfoColGroup 
estimateCompressedColGroupSize(int[] colIndexes, int nrUniqueUpperBound);
 
        /**
         * Method used to extract the CompressedSizeEstimationFactors from an 
constructed UncompressedBitmap. Note this
         * method works both for the sample based estimator and the exact 
estimator, since the bitmap, can be extracted from
         * a sample or from the entire dataset.
         * 
-        * @param ubm        The UncompressedBitmap, either extracted from a 
sample or from the entier dataset
+        * @param ubm        The UncompressedBitmap, either extracted from a 
sample or from the entire dataset
         * @param colIndexes The columns that is compressed together.
         * @return The size factors estimated from the Bit Map.
         */
@@ -154,16 +218,21 @@ public abstract class CompressedSizeEstimator {
 
        private static class SizeEstimationTask implements 
Callable<CompressedSizeInfoColGroup> {
                private final CompressedSizeEstimator _estimator;
-               private final int _col;
+               private final int[] _cols;
 
                protected SizeEstimationTask(CompressedSizeEstimator estimator, 
int col) {
                        _estimator = estimator;
-                       _col = col;
+                       _cols = new int[] {col};
+               }
+
+               protected SizeEstimationTask(CompressedSizeEstimator estimator, 
int[] cols) {
+                       _estimator = estimator;
+                       _cols = cols;
                }
 
                @Override
                public CompressedSizeInfoColGroup call() {
-                       return _estimator.estimateCompressedColGroupSize(new 
int[] {_col});
+                       return _estimator.estimateCompressedColGroupSize(_cols);
                }
        }
 
@@ -174,8 +243,4 @@ public abstract class CompressedSizeEstimator {
                }
                return colIndexes;
        }
-
-       public MatrixBlock getSample() {
-               return _data;
-       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorExact.java
 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorExact.java
index 40677e9..5fdf8e2 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorExact.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorExact.java
@@ -34,7 +34,8 @@ public class CompressedSizeEstimatorExact extends 
CompressedSizeEstimator {
        }
 
        @Override
-       public CompressedSizeInfoColGroup estimateCompressedColGroupSize(int[] 
colIndexes) {
+       public CompressedSizeInfoColGroup estimateCompressedColGroupSize(int[] 
colIndexes, int nrUniqueUpperBound) {
+               // exact estimator can ignore upper bound.
                ABitmap entireBitMap = BitmapEncoder.extractBitmap(colIndexes, 
_data, _transposed);
                return new 
CompressedSizeInfoColGroup(estimateCompressedColGroupSize(entireBitMap, 
colIndexes),
                        _cs.validCompressions);
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorFactory.java
 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorFactory.java
index cf5437e..ebeef16 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorFactory.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorFactory.java
@@ -27,23 +27,42 @@ import org.apache.sysds.runtime.matrix.data.MatrixBlock;
 public class CompressedSizeEstimatorFactory {
        protected static final Log LOG = 
LogFactory.getLog(CompressedSizeEstimatorFactory.class.getName());
 
-       public static final int minimumSampleSize = 2000;
-
        public static CompressedSizeEstimator getSizeEstimator(MatrixBlock 
data, CompressionSettings cs) {
 
-               final long nRows = cs.transposed ? data.getNumColumns() : 
data.getNumRows();
+               final int nRows = cs.transposed ? data.getNumColumns() : 
data.getNumRows();
+               final int nCols = cs.transposed ? data.getNumRows() : 
data.getNumColumns();
+               final int nnzRows = (int) Math.ceil(data.getNonZeros() / nCols);
                
-               // Calculate the sample size.
-               // If the sample size is very small, set it to the minimum size
-               final int sampleSize = Math.max((int) Math.ceil(nRows * 
cs.samplingRatio), minimumSampleSize);
+               final double sampleRatio = cs.samplingRatio;
+               final int sampleSize = getSampleSize(sampleRatio, nRows, 
cs.minimumSampleSize);
 
-               CompressedSizeEstimator est;
-               if(cs.samplingRatio >= 1.0 || nRows < minimumSampleSize || 
sampleSize > nRows)
-                       est = new CompressedSizeEstimatorExact(data, cs);
-               else
-                       est = new CompressedSizeEstimatorSample(data, cs, 
sampleSize);
+               final CompressedSizeEstimator est = 
(shouldUseExactEstimator(cs, nRows, sampleSize,
+                       nnzRows)) ? new CompressedSizeEstimatorExact(data,
+                               cs) : tryToMakeSampleEstimator(data, cs, 
sampleRatio, sampleSize, nRows, nnzRows);
 
                LOG.debug("Estimating using: " + est);
                return est;
        }
+
+       private static CompressedSizeEstimator 
tryToMakeSampleEstimator(MatrixBlock data, CompressionSettings cs,
+               double sampleRatio, int sampleSize, int nRows, int nnzRows) {
+               CompressedSizeEstimatorSample estS = new 
CompressedSizeEstimatorSample(data, cs, sampleSize);
+               while(estS.getSample() == null) {
+                       LOG.warn("Doubling sample size");
+                       sampleSize = sampleSize * 2;
+                       if(shouldUseExactEstimator(cs, nRows, sampleSize, 
nnzRows))
+                               return new CompressedSizeEstimatorExact(data, 
cs);
+                       else
+                               estS.sampleData(sampleSize);
+               }
+               return estS;
+       }
+
+       private static boolean shouldUseExactEstimator(CompressionSettings cs, 
int nRows, int sampleSize, int nnzRows) {
+               return cs.samplingRatio >= 1.0 || nRows < cs.minimumSampleSize 
|| sampleSize > nnzRows;
+       }
+
+       private static int getSampleSize(double sampleRatio, int nRows, int 
minimumSampleSize) {
+               return Math.max((int) Math.ceil(nRows * sampleRatio), 
minimumSampleSize);
+       }
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorSample.java
 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorSample.java
index 3098394..9fe57d7 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorSample.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeEstimatorSample.java
@@ -21,7 +21,6 @@ package org.apache.sysds.runtime.compress.estim;
 
 import java.util.HashMap;
 
-import org.apache.sysds.runtime.DMLCompressionException;
 import org.apache.sysds.runtime.compress.CompressionSettings;
 import org.apache.sysds.runtime.compress.colgroup.AColGroup.CompressionType;
 import org.apache.sysds.runtime.compress.estim.sample.HassAndStokes;
@@ -38,8 +37,8 @@ import org.apache.sysds.runtime.util.UtilFunctions;
 
 public class CompressedSizeEstimatorSample extends CompressedSizeEstimator {
 
-       private final int[] _sampleRows;
-       private final MatrixBlock _sample;
+       private int[] _sampleRows;
+       private MatrixBlock _sample;
        private HashMap<Integer, Double> _solveCache = null;
 
        /**
@@ -51,12 +50,16 @@ public class CompressedSizeEstimatorSample extends 
CompressedSizeEstimator {
         */
        public CompressedSizeEstimatorSample(MatrixBlock data, 
CompressionSettings cs, int sampleSize) {
                super(data, cs);
-               _sampleRows = 
CompressedSizeEstimatorSample.getSortedUniformSample(_numRows, sampleSize, 
_cs.seed);
-               _solveCache = new HashMap<>();
-               _sample = sampleData();
+               _sample = sampleData(sampleSize);
        }
 
-       protected MatrixBlock sampleData() {
+       public MatrixBlock getSample() {
+               return _sample;
+       }
+
+       public MatrixBlock sampleData(int sampleSize) {
+               _sampleRows = 
CompressedSizeEstimatorSample.getSortedUniformSample(_numRows, sampleSize, 
_cs.seed);
+               _solveCache = new HashMap<>();
                MatrixBlock sampledMatrixBlock;
                if(_data.isInSparseFormat() && !_cs.transposed) {
                        sampledMatrixBlock = new 
MatrixBlock(_sampleRows.length, _data.getNumColumns(), true);
@@ -77,18 +80,17 @@ public class CompressedSizeEstimatorSample extends 
CompressedSizeEstimator {
                                select.appendValue(_sampleRows[i], 0, 1);
 
                        sampledMatrixBlock = _data.removeEmptyOperations(new 
MatrixBlock(), !_cs.transposed, true, select);
-
                }
 
                if(sampledMatrixBlock.isEmpty())
-                       throw new DMLCompressionException("Empty sample block");
-
-               return sampledMatrixBlock;
+                       return null;
+               else
+                       return sampledMatrixBlock;
 
        }
 
        @Override
-       public CompressedSizeInfoColGroup estimateCompressedColGroupSize(int[] 
colIndexes) {
+       public CompressedSizeInfoColGroup estimateCompressedColGroupSize(int[] 
colIndexes, int nrUniqueUpperBound) {
                final int sampleSize = _sampleRows.length;
                // final int numCols = colIndexes.length;
                final double scalingFactor = ((double) _numRows / sampleSize);
@@ -109,7 +111,7 @@ public class CompressedSizeEstimatorSample extends 
CompressedSizeEstimator {
                // Estimate number of distinct values (incl fixes for anomalies 
w/ large sample fraction)
                int totalCardinality = getNumDistinctValues(ubm, _numRows, 
sampleSize, _solveCache);
                // Number of unique is trivially bounded by the sampled number 
of uniques and the number of rows.
-               totalCardinality = Math.min(Math.max(totalCardinality, 
fact.numVals), _numRows);
+               totalCardinality = Math.min(Math.min(Math.max(totalCardinality, 
fact.numVals), _numRows), nrUniqueUpperBound);
 
                // estimate number of non-zeros (conservatively round up)
                final double C = Math.max(1 - (double) fact.numSingle / 
sampleSize, (double) sampleSize / _numRows);
@@ -127,7 +129,6 @@ public class CompressedSizeEstimatorSample extends 
CompressedSizeEstimator {
                for(IntArrayList a : ubm.getOffsetList())
                        if(a.size() > largestInstanceCount)
                                largestInstanceCount = a.size();
-               
 
                final boolean zeroIsMostFrequent = largestInstanceCount == 
numZerosInSample;
 
@@ -307,12 +308,12 @@ public class CompressedSizeEstimatorSample extends 
CompressedSizeEstimator {
        /**
         * Returns a sorted array of n integers, drawn uniformly from the range 
[0,range).
         * 
-        * @param range    the range
-        * @param smplSize sample size
+        * @param range      the range
+        * @param sampleSize sample size
         * @return sorted array of integers
         */
-       private static int[] getSortedUniformSample(int range, int smplSize, 
long seed) {
-               return UtilFunctions.getSortedSampleIndexes(range, smplSize, 
seed);
+       private static int[] getSortedUniformSample(int range, int sampleSize, 
long seed) {
+               return UtilFunctions.getSortedSampleIndexes(range, sampleSize, 
seed);
        }
 
        @Override
@@ -329,4 +330,5 @@ public class CompressedSizeEstimatorSample extends 
CompressedSizeEstimator {
                sb.append(_numRows);
                return sb.toString();
        }
+
 }
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeInfoColGroup.java
 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeInfoColGroup.java
index 50aeb7e..8b984ff 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeInfoColGroup.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/estim/CompressedSizeInfoColGroup.java
@@ -27,6 +27,8 @@ import java.util.Set;
 import org.apache.commons.lang.NotImplementedException;
 import org.apache.commons.logging.Log;
 import org.apache.commons.logging.LogFactory;
+import org.apache.sysds.runtime.compress.CompressionSettings;
+import 
org.apache.sysds.runtime.compress.cocode.PlanningCoCoder.PartitionerType;
 import org.apache.sysds.runtime.compress.colgroup.AColGroup.CompressionType;
 import org.apache.sysds.runtime.compress.colgroup.ColGroupSizes;
 
@@ -59,7 +61,7 @@ public class CompressedSizeInfoColGroup {
                _cardinalityRatio = (double) numVals / numRows;
                _sizes = null;
                _bestCompressionType = null;
-               _minSize = 
ColGroupSizes.estimateInMemorySizeDDC(columns.length, numVals, numRows, false);
+               _minSize = 
ColGroupSizes.estimateInMemorySizeDDC(columns.length, numVals, numRows, 1.0, 
false);
        }
 
        /**
@@ -106,6 +108,15 @@ public class CompressedSizeInfoColGroup {
                return _sizes.get(ct);
        }
 
+       public CompressionType getBestCompressionType(CompressionSettings cs) {
+               if(cs.columnPartitioner == PartitionerType.COST_MATRIX_MULT) {
+                       // if(_sizes.get(CompressionType.SDC) * 0.8 < 
_sizes.get(_bestCompressionType))
+                       if(getMostCommonFraction() > 0.4)
+                               return CompressionType.SDC;
+               }
+               return _bestCompressionType;
+       }
+
        public CompressionType getBestCompressionType() {
                return _bestCompressionType;
        }
@@ -171,26 +182,28 @@ public class CompressedSizeInfoColGroup {
                        case DDC:
                                // + 1 if the column contains zero
                                return 
ColGroupSizes.estimateInMemorySizeDDC(numCols,
-                                       fact.numVals + (fact.numOffs < 
fact.numRows ? 1 : 0), fact.numRows, fact.lossy);
+                                       fact.numVals + (fact.numOffs < 
fact.numRows ? 1 : 0), fact.numRows, fact.tupleSparsity, fact.lossy);
                        case RLE:
                                return 
ColGroupSizes.estimateInMemorySizeRLE(numCols, fact.numVals, fact.numRuns, 
fact.numRows,
-                                       fact.lossy);
+                                       fact.tupleSparsity, fact.lossy);
                        case OLE:
                                return 
ColGroupSizes.estimateInMemorySizeOLE(numCols, fact.numVals, fact.numOffs + 
fact.numVals,
-                                       fact.numRows, fact.lossy);
+                                       fact.numRows, fact.tupleSparsity, 
fact.lossy);
                        case UNCOMPRESSED:
                                return 
ColGroupSizes.estimateInMemorySizeUncompressed(fact.numRows, numCols, 
fact.overAllSparsity);
                        case SDC:
                                if(fact.numOffs <= 1)
                                        return 
ColGroupSizes.estimateInMemorySizeSDCSingle(numCols, fact.numVals, fact.numRows,
-                                               fact.largestOff, 
fact.zeroIsMostFrequent, fact.containNoZeroValues, fact.lossy);
+                                               fact.largestOff, 
fact.zeroIsMostFrequent, fact.containNoZeroValues, fact.tupleSparsity,
+                                               fact.lossy);
                                return 
ColGroupSizes.estimateInMemorySizeSDC(numCols, fact.numVals, fact.numRows, 
fact.largestOff,
-                                       fact.zeroIsMostFrequent, 
fact.containNoZeroValues, fact.lossy);
+                                       fact.zeroIsMostFrequent, 
fact.containNoZeroValues, fact.tupleSparsity, fact.lossy);
                        case CONST:
                                if(fact.numOffs == 0)
                                        return 
ColGroupSizes.estimateInMemorySizeEMPTY(numCols);
                                else if(fact.numOffs == fact.numRows && 
fact.numVals == 1)
-                                       return 
ColGroupSizes.estimateInMemorySizeCONST(numCols, fact.numVals, fact.lossy);
+                                       return 
ColGroupSizes.estimateInMemorySizeCONST(numCols, fact.numVals, 
fact.tupleSparsity,
+                                               fact.lossy);
                                else
                                        return -1;
                        default:
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapEncoder.java 
b/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapEncoder.java
index 310b236..64b0bdd 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapEncoder.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapEncoder.java
@@ -34,6 +34,7 @@ import 
org.apache.sysds.runtime.compress.utils.DblArrayIntListHashMap.DArrayILis
 import org.apache.sysds.runtime.compress.utils.DoubleIntListHashMap;
 import 
org.apache.sysds.runtime.compress.utils.DoubleIntListHashMap.DIListEntry;
 import org.apache.sysds.runtime.compress.utils.IntArrayList;
+import org.apache.sysds.runtime.compress.utils.MultiColBitmap;
 import org.apache.sysds.runtime.data.SparseBlock;
 import org.apache.sysds.runtime.matrix.data.MatrixBlock;
 
@@ -52,29 +53,28 @@ public class BitmapEncoder {
         * @param transposed Boolean specifying if the rawblock was transposed.
         * @return uncompressed bitmap representation of the columns
         */
-       public static Bitmap extractBitmap(int[] colIndices, MatrixBlock 
rawBlock, boolean transposed) {
-
-               Bitmap res = null;
-               if(colIndices.length == 1) {
-                       res = extractBitmap(colIndices[0], rawBlock, 
transposed);
-               }
-               // multiple column selection (general case)
-               else {
+       public static ABitmap extractBitmap(int[] colIndices, MatrixBlock 
rawBlock, boolean transposed) {
+               try {
                        final int numRows = transposed ? 
rawBlock.getNumColumns() : rawBlock.getNumRows();
-                       try {
-                               res = extractBitmap(colIndices, 
ReaderColumnSelection.createReader(rawBlock, colIndices, transposed), numRows);
-                       }
-                       catch(Exception e) {
-                               throw new DMLRuntimeException("Failed to 
extract bitmap", e);
+                       if(rawBlock.isEmpty() && colIndices.length == 1)
+                               return new Bitmap(null, null, numRows);
+                       else if(colIndices.length == 1)
+                               return extractBitmap(colIndices[0], rawBlock, 
transposed);
+                       else if(rawBlock.isEmpty())
+                               return new MultiColBitmap(colIndices.length, 
null, null, numRows);
+                       else {
+                               ReaderColumnSelection reader = 
ReaderColumnSelection.createReader(rawBlock, colIndices, transposed);
+                               return extractBitmap(colIndices, reader, 
numRows);
                        }
                }
-               return res;
-
+               catch(Exception e) {
+                       throw new DMLRuntimeException("Failed to extract 
bitmap", e);
+               }
        }
 
        public static ABitmap extractBitmap(int[] colIndices, int rows, BitSet 
rawBlock, CompressionSettings compSettings) {
                ReaderColumnSelection reader = new 
ReaderColumnSelectionBitSet(rawBlock, rows, colIndices);
-               Bitmap res = extractBitmap(colIndices, reader, rows);
+               ABitmap res = extractBitmap(colIndices, reader, rows);
                return res;
        }
 
@@ -88,7 +88,7 @@ public class BitmapEncoder {
         * @param transposed Boolean specifying if the rawBlock is transposed 
or not.
         * @return Bitmap containing the Information of the column.
         */
-       private static Bitmap extractBitmap(int colIndex, MatrixBlock rawBlock, 
boolean transposed) {
+       private static ABitmap extractBitmap(int colIndex, MatrixBlock 
rawBlock, boolean transposed) {
                DoubleIntListHashMap hashMap = transposed ? 
extractHashMapTransposed(colIndex,
                        rawBlock) : extractHashMap(colIndex, rawBlock);
                return makeBitmap(hashMap, transposed ? 
rawBlock.getNumColumns() : rawBlock.getNumRows());
@@ -187,7 +187,7 @@ public class BitmapEncoder {
         * @param numRows    The number of contained rows
         * @return The Bitmap
         */
-       protected static Bitmap extractBitmap(int[] colIndices, 
ReaderColumnSelection rowReader, int numRows) {
+       protected static ABitmap extractBitmap(int[] colIndices, 
ReaderColumnSelection rowReader, int numRows) {
                // probe map for distinct items (for value or value groups)
                DblArrayIntListHashMap distinctVals = new 
DblArrayIntListHashMap();
 
@@ -216,24 +216,24 @@ public class BitmapEncoder {
         * @param numCols      Number of columns
         * @return The Bitmap.
         */
-       private static Bitmap makeBitmap(DblArrayIntListHashMap distinctVals, 
int numRows, int numCols) {
+       private static ABitmap makeBitmap(DblArrayIntListHashMap distinctVals, 
int numRows, int numCols) {
                // added for one pass bitmap construction
                // Convert inputs to arrays
                ArrayList<DArrayIListEntry> mapEntries = 
distinctVals.extractValues();
                if(!mapEntries.isEmpty()) {
                        int numVals = distinctVals.size();
-                       double[] values = new double[numVals * numCols];
+                       double[][] values = new double[numVals][];
                        IntArrayList[] offsetsLists = new IntArrayList[numVals];
                        int bitmapIx = 0;
                        for(DArrayIListEntry val : mapEntries) {
-                               System.arraycopy(val.key.getData(), 0, values, 
bitmapIx * numCols, numCols);
+                               values[bitmapIx] = val.key.getData();
                                offsetsLists[bitmapIx++] = val.value;
                        }
 
-                       return new Bitmap(numCols, offsetsLists, values, 
numRows);
+                       return new MultiColBitmap(numCols, offsetsLists, 
values, numRows);
                }
                else
-                       return new Bitmap(numCols, null, null, numRows);
+                       return new MultiColBitmap(numCols, null, null, numRows);
 
        }
 
@@ -248,7 +248,7 @@ public class BitmapEncoder {
                // added for one pass bitmap construction
                // Convert inputs to arrays
                int numVals = distinctVals.size();
-               if(numVals > 0){
+               if(numVals > 0) {
 
                        double[] values = new double[numVals];
                        IntArrayList[] offsetsLists = new IntArrayList[numVals];
@@ -257,11 +257,11 @@ public class BitmapEncoder {
                                values[bitmapIx] = val.key;
                                offsetsLists[bitmapIx++] = val.value;
                        }
-       
-                       return new Bitmap(1, offsetsLists, values, numRows);
+
+                       return new Bitmap(offsetsLists, values, numRows);
                }
-               else{
-                       return new Bitmap(1, null, null, numRows);
+               else {
+                       return new Bitmap(null, null, numRows);
                }
        }
 
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapLossyEncoder.java 
b/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapLossyEncoder.java
index 81789f1..4e74d69 100644
--- 
a/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapLossyEncoder.java
+++ 
b/src/main/java/org/apache/sysds/runtime/compress/lib/BitmapLossyEncoder.java
@@ -30,6 +30,7 @@ import java.util.Map;
 import java.util.Map.Entry;
 import java.util.Queue;
 
+import org.apache.commons.lang.NotImplementedException;
 import org.apache.commons.logging.Log;
 import org.apache.commons.logging.LogFactory;
 import org.apache.sysds.runtime.compress.CompressedMatrixBlock;
@@ -68,20 +69,21 @@ public class BitmapLossyEncoder {
         * @param numRows The number of rows contained in the ubm.
         * @return A bitmap.
         */
-       public static ABitmap makeBitmapLossy(Bitmap ubm, int numRows) {
-               final double[] fp = ubm.getValues();
-               if(fp.length == 0) {
-                       return ubm;
-               }
-               Stats stats = new Stats(fp);
-               // TODO make better decisions than just a 8 Bit encoding.
-               if(Double.isInfinite(stats.max) || 
Double.isInfinite(stats.min)) {
-                       LOG.warn("Defaulting to incompressable colGroup");
-                       return ubm;
-               }
-               else {
-                       return make8BitLossy(ubm, stats, numRows);
-               }
+       public static ABitmap makeBitmapLossy(ABitmap ubm, int numRows) {
+               throw new NotImplementedException();
+               // final double[] fp = ubm.getValues();
+               // if(fp.length == 0) {
+               //      return ubm;
+               // }
+               // Stats stats = new Stats(fp);
+               // // TODO make better decisions than just a 8 Bit encoding.
+               // if(Double.isInfinite(stats.max) || 
Double.isInfinite(stats.min)) {
+               //      LOG.warn("Defaulting to incompressable colGroup");
+               //      return ubm;
+               // }
+               // else {
+               //      return make8BitLossy(ubm, stats, numRows);
+               // }
        }
 
        /**
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibLeftMultBy.java 
b/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibLeftMultBy.java
index 9c73f7c..ba22642 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibLeftMultBy.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibLeftMultBy.java
@@ -255,7 +255,7 @@ public class CLALibLeftMultBy {
                                ExecutorService pool = CommonThreadPool.get(k);
                                // compute remaining compressed column groups 
in parallel
                                ArrayList<Callable<Object>> tasks = new 
ArrayList<>();
-                               int rowBlockSize = 8;
+                               int rowBlockSize = 1;
                                if(overlapping) {
                                        for(int blo = 0; blo < 
that.getNumRows(); blo += rowBlockSize) {
                                                tasks.add(new 
LeftMatrixMatrixMultTask(colGroups, that, ret, blo,
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibRightMultBy.java 
b/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibRightMultBy.java
index 5b0a105..61e275c 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibRightMultBy.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibRightMultBy.java
@@ -141,14 +141,14 @@ public class CLALibRightMultBy {
                        ret.setOverlapping(true);
 
                if(containsNull) {
-                       ColGroupEmpty cge = 
findEmptyColumnsAndMakeEmptyColGroup(retCg, ret.getNumColumns());
+                       ColGroupEmpty cge = 
findEmptyColumnsAndMakeEmptyColGroup(retCg, ret.getNumColumns(), 
ret.getNumRows());
                        if(cge != null)
                                retCg.add(cge);
                }
                return ret;
        }
 
-       private static ColGroupEmpty 
findEmptyColumnsAndMakeEmptyColGroup(List<AColGroup> colGroups, int nCols) {
+       private static ColGroupEmpty 
findEmptyColumnsAndMakeEmptyColGroup(List<AColGroup> colGroups, int nCols, int 
nRows) {
                Set<Integer> emptyColumns = new HashSet<Integer>(nCols);
                for(int i = 0; i < nCols; i++)
                        emptyColumns.add(i);
@@ -159,7 +159,7 @@ public class CLALibRightMultBy {
 
                if(emptyColumns.size() != 0) {
                        int[] emptyColumnsFinal = 
emptyColumns.stream().mapToInt(Integer::intValue).toArray();
-                       return new ColGroupEmpty(emptyColumnsFinal, 
colGroups.get(0).getNumRows());
+                       return new ColGroupEmpty(emptyColumnsFinal, nRows);
                }
                else
                        return null;
diff --git 
a/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibSquash.java 
b/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibSquash.java
index aacea4a..fecd08e 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibSquash.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/lib/CLALibSquash.java
@@ -39,7 +39,6 @@ import 
org.apache.sysds.runtime.compress.colgroup.ColGroupFactory;
 import org.apache.sysds.runtime.compress.colgroup.ColGroupValue;
 import org.apache.sysds.runtime.compress.readers.ReaderColumnSelection;
 import org.apache.sysds.runtime.compress.utils.ABitmap;
-import org.apache.sysds.runtime.compress.utils.Bitmap;
 import org.apache.sysds.runtime.util.CommonThreadPool;
 
 public class CLALibSquash {
@@ -123,18 +122,16 @@ public class CLALibSquash {
                        map = extractBitmap(columnIds, m);
                }
                else
-                       map = 
BitmapLossyEncoder.extractMapFromCompressedSingleColumn(m,
-                               columnIds[0],
-                               minMaxes[columnIds[0] * 2],
+                       map = 
BitmapLossyEncoder.extractMapFromCompressedSingleColumn(m, columnIds[0], 
minMaxes[columnIds[0] * 2],
                                minMaxes[columnIds[0] * 2 + 1], m.getNumRows());
 
-               AColGroup newGroup = ColGroupFactory.compress(columnIds, 
m.getNumRows(), map, CompressionType.DDC, cs, m);
+               AColGroup newGroup = ColGroupFactory.compress(columnIds, 
m.getNumRows(), map, CompressionType.DDC, cs, m, 1);
                return newGroup;
        }
 
        private static ABitmap extractBitmap(int[] colIndices, 
CompressedMatrixBlock compressedBlock) {
-               Bitmap x = BitmapEncoder.extractBitmap(colIndices,
-                       
ReaderColumnSelection.createCompressedReader(compressedBlock, colIndices),  
compressedBlock.getNumRows());
+               ABitmap x = BitmapEncoder.extractBitmap(colIndices,
+                       
ReaderColumnSelection.createCompressedReader(compressedBlock, colIndices), 
compressedBlock.getNumRows());
                return BitmapLossyEncoder.makeBitmapLossy(x, 
compressedBlock.getNumRows());
        }
 
diff --git a/src/main/java/org/apache/sysds/runtime/compress/utils/Bitmap.java 
b/src/main/java/org/apache/sysds/runtime/compress/utils/Bitmap.java
index 09354f6..db0c2b6 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/utils/Bitmap.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/utils/Bitmap.java
@@ -34,8 +34,8 @@ public final class Bitmap extends ABitmap {
         */
        private double[] _values;
 
-       public Bitmap(int numCols, IntArrayList[] offsetsLists, double[] 
values, int rows) {
-               super(numCols, offsetsLists, rows);
+       public Bitmap(IntArrayList[] offsetsLists, double[] values, int rows) {
+               super(1, offsetsLists, rows);
                _values = values;
        }
 
@@ -48,33 +48,16 @@ public final class Bitmap extends ABitmap {
                return _values;
        }
 
-       /**
-        * Obtain tuple of column values associated with index.
-        * 
-        * @param ix index of a particular distinct value
-        * @return the tuple of column values associated with the specified 
index
-        */
-       public double[] getValues(int ix) {
-               return Arrays.copyOfRange(_values, ix * _numCols, (ix + 1) * 
_numCols);
-       }
-
        public int getNumNonZerosInOffset(int idx){
-               if(_numCols == 1)
-                       return  _values[0] != 0 ? 1 : 0;
-               int nz = 0;
-               for(int i = idx * _numCols; i < (idx+1) * _numCols; i++)
-                       nz += _values[i] == 0 ? 0 : 1;
-               
-               return nz;
+               return  _values[idx] != 0 ? 1 : 0;
        }
 
        public int getNumValues() {
-               return (_values == null) ? 0: _values.length / _numCols;
+               return (_values == null) ? 0: _values.length;
        }
 
        public void sortValuesByFrequency() {
                int numVals = getNumValues();
-               int numCols = getNumColumns();
 
                double[] freq = new double[numVals];
                int[] pos = new int[numVals];
@@ -90,10 +73,10 @@ public final class Bitmap extends ABitmap {
                ArrayUtils.reverse(pos);
 
                // create new value and offset list arrays
-               double[] lvalues = new double[numVals * numCols];
+               double[] lvalues = new double[numVals];
                IntArrayList[] loffsets = new IntArrayList[numVals];
                for(int i = 0; i < numVals; i++) {
-                       System.arraycopy(_values, pos[i] * numCols, lvalues, i 
* numCols, numCols);
+                       lvalues[i]  = _values[pos[i]];
                        loffsets[i] = _offsetsLists[pos[i]];
                }
                _values = lvalues;
diff --git a/src/main/java/org/apache/sysds/runtime/compress/utils/Bitmap.java 
b/src/main/java/org/apache/sysds/runtime/compress/utils/MultiColBitmap.java
similarity index 70%
copy from src/main/java/org/apache/sysds/runtime/compress/utils/Bitmap.java
copy to 
src/main/java/org/apache/sysds/runtime/compress/utils/MultiColBitmap.java
index 09354f6..80d98df 100644
--- a/src/main/java/org/apache/sysds/runtime/compress/utils/Bitmap.java
+++ b/src/main/java/org/apache/sysds/runtime/compress/utils/MultiColBitmap.java
@@ -27,14 +27,12 @@ import org.apache.sysds.runtime.util.SortUtils;
 /**
  * Uncompressed representation of one or more columns in bitmap format.
  */
-public final class Bitmap extends ABitmap {
+public final class MultiColBitmap extends ABitmap {
 
-       /**
-        * Distinct values that appear in the column. Linearized as value 
groups <v11 v12> <v21 v22>.
-        */
-       private double[] _values;
+       /** Distinct tuples that appear in the columnGroup */
+       private double[][] _values;
 
-       public Bitmap(int numCols, IntArrayList[] offsetsLists, double[] 
values, int rows) {
+       public MultiColBitmap(int numCols, IntArrayList[] offsetsLists, 
double[][] values, int rows) {
                super(numCols, offsetsLists, rows);
                _values = values;
        }
@@ -44,7 +42,7 @@ public final class Bitmap extends ABitmap {
         * 
         * @return dictionary of value tuples
         */
-       public double[] getValues() {
+       public double[][] getValues() {
                return _values;
        }
 
@@ -55,29 +53,26 @@ public final class Bitmap extends ABitmap {
         * @return the tuple of column values associated with the specified 
index
         */
        public double[] getValues(int ix) {
-               return Arrays.copyOfRange(_values, ix * _numCols, (ix + 1) * 
_numCols);
+               return _values[ix];
        }
 
-       public int getNumNonZerosInOffset(int idx){
-               if(_numCols == 1)
-                       return  _values[0] != 0 ? 1 : 0;
+       public int getNumNonZerosInOffset(int idx) {
                int nz = 0;
-               for(int i = idx * _numCols; i < (idx+1) * _numCols; i++)
-                       nz += _values[i] == 0 ? 0 : 1;
-               
+               for(double v : getValues(idx))
+                       nz += v == 0 ? 0 : 1;
+
                return nz;
        }
 
        public int getNumValues() {
-               return (_values == null) ? 0: _values.length / _numCols;
+               return (_values == null) ? 0 : _values.length;
        }
 
        public void sortValuesByFrequency() {
-               int numVals = getNumValues();
-               int numCols = getNumColumns();
-
-               double[] freq = new double[numVals];
-               int[] pos = new int[numVals];
+               final int numVals = getNumValues();
+               
+               final double[] freq = new double[numVals];
+               final int[] pos = new int[numVals];
 
                // populate the temporary arrays
                for(int i = 0; i < numVals; i++) {
@@ -90,10 +85,10 @@ public final class Bitmap extends ABitmap {
                ArrayUtils.reverse(pos);
 
                // create new value and offset list arrays
-               double[] lvalues = new double[numVals * numCols];
+               double[][] lvalues = new double[numVals][];
                IntArrayList[] loffsets = new IntArrayList[numVals];
                for(int i = 0; i < numVals; i++) {
-                       System.arraycopy(_values, pos[i] * numCols, lvalues, i 
* numCols, numCols);
+                       lvalues[i]  = _values[pos[i]];
                        loffsets[i] = _offsetsLists[pos[i]];
                }
                _values = lvalues;
@@ -104,7 +99,9 @@ public final class Bitmap extends ABitmap {
        public String toString() {
                StringBuilder sb = new StringBuilder();
                sb.append(super.toString());
-               sb.append("\nValues: " + Arrays.toString(_values));
+               sb.append("\nValues:");
+               for(double[] vv : _values)
+                       sb.append("\n" + Arrays.toString(vv));
                return sb.toString();
        }
 
diff --git a/src/main/java/org/apache/sysds/utils/MemoryEstimates.java 
b/src/main/java/org/apache/sysds/utils/MemoryEstimates.java
index 8401d1a..8e0bac8 100644
--- a/src/main/java/org/apache/sysds/utils/MemoryEstimates.java
+++ b/src/main/java/org/apache/sysds/utils/MemoryEstimates.java
@@ -29,6 +29,8 @@ package org.apache.sysds.utils;
  */
 public class MemoryEstimates {
 
+       // private static final Log LOG = 
LogFactory.getLog(MemoryEstimates.class.getName());
+
        /**
         * Get the worst case memory usage of an java.util.BitSet java object.
         * 
diff --git 
a/src/test/java/org/apache/sysds/test/component/compress/AbstractCompressedUnaryTests.java
 
b/src/test/java/org/apache/sysds/test/component/compress/AbstractCompressedUnaryTests.java
index 94ba730..80df1e5 100644
--- 
a/src/test/java/org/apache/sysds/test/component/compress/AbstractCompressedUnaryTests.java
+++ 
b/src/test/java/org/apache/sysds/test/component/compress/AbstractCompressedUnaryTests.java
@@ -228,9 +228,6 @@ public abstract class AbstractCompressedUnaryTests extends 
CompressedTestBase {
                        }
 
                }
-               catch(NotImplementedException e) {
-                       throw e;
-               }
                catch(Exception e) {
                        e.printStackTrace();
                        throw new RuntimeException(this.toString() + "\n" + 
e.getMessage(), e);
diff --git 
a/src/test/java/org/apache/sysds/test/component/compress/CompressedTestBase.java
 
b/src/test/java/org/apache/sysds/test/component/compress/CompressedTestBase.java
index 1167512..7b9d871 100644
--- 
a/src/test/java/org/apache/sysds/test/component/compress/CompressedTestBase.java
+++ 
b/src/test/java/org/apache/sysds/test/component/compress/CompressedTestBase.java
@@ -78,7 +78,7 @@ public abstract class CompressedTestBase extends TestBase {
        protected static SparsityType[] usedSparsityTypes = new SparsityType[] 
{SparsityType.FULL, SparsityType.SPARSE,};
 
        protected static ValueType[] usedValueTypes = new ValueType[] 
{ValueType.RAND_ROUND, ValueType.OLE_COMPRESSIBLE,
-               ValueType.RLE_COMPRESSIBLE,};
+               ValueType.RLE_COMPRESSIBLE};
 
        protected static ValueRange[] usedValueRanges = new ValueRange[] 
{ValueRange.SMALL, ValueRange.NEGATIVE,
                ValueRange.BYTE};
@@ -120,6 +120,9 @@ public abstract class CompressedTestBase extends TestBase {
                new 
CompressionSettingsBuilder().setSamplingRatio(0.1).setSeed(compressionSeed).setTransposeInput("true")
                        
.setColumnPartitioner(PartitionerType.STATIC).setInvestigateEstimate(true),
 
+               new 
CompressionSettingsBuilder().setSamplingRatio(0.1).setSeed(compressionSeed).setTransposeInput("true")
+                       
.setColumnPartitioner(PartitionerType.COST_MATRIX_MULT).setInvestigateEstimate(true),
+
                // Forced Uncompressed tests
                new 
CompressionSettingsBuilder().setValidCompressions(EnumSet.of(CompressionType.UNCOMPRESSED)),
 
@@ -302,6 +305,8 @@ public abstract class CompressedTestBase extends TestBase {
                                for(OverLapping ov : overLapping) {
                                        tests.add(new Object[] 
{SparsityType.EMPTY, ValueType.RAND, ValueRange.BOOLEAN, cs, mt, ov});
                                        tests.add(new Object[] 
{SparsityType.FULL, ValueType.CONST, ValueRange.LARGE, cs, mt, ov});
+                                       tests.add(
+                                               new Object[] 
{SparsityType.FULL, ValueType.ONE_HOT_ENCODED, ValueRange.BOOLEAN, cs, mt, ov});
                                }
                return tests;
        }
diff --git 
a/src/test/java/org/apache/sysds/test/component/compress/CompressibleInputGenerator.java
 
b/src/test/java/org/apache/sysds/test/component/compress/CompressibleInputGenerator.java
index 4666327..a8a2a3e 100644
--- 
a/src/test/java/org/apache/sysds/test/component/compress/CompressibleInputGenerator.java
+++ 
b/src/test/java/org/apache/sysds/test/component/compress/CompressibleInputGenerator.java
@@ -82,6 +82,21 @@ public class CompressibleInputGenerator {
                return output;
        }
 
+       public static double[][] getInputOneHotMatrix(int rows, int cols, int 
seed) {
+               double[][] variations = new double[cols][];
+               for(int i = 0; i < cols; i++) {
+                       variations[i] = new double[cols];
+                       variations[i][i] = 1;
+               }
+
+               double[][] matrix = new double[rows][];
+               Random r = new Random(seed);
+               for(int i = 0; i < rows; i++)
+                       matrix[i] = variations[r.nextInt(cols)];
+
+               return matrix;
+       }
+
        private static double[][] rle(int rows, int cols, int nrUnique, int 
max, int min, double sparsity, int seed,
                boolean transpose) {
 
diff --git 
a/src/test/java/org/apache/sysds/test/component/compress/TestBase.java 
b/src/test/java/org/apache/sysds/test/component/compress/TestBase.java
index f2ebbba..29a2a87 100644
--- a/src/test/java/org/apache/sysds/test/component/compress/TestBase.java
+++ b/src/test/java/org/apache/sysds/test/component/compress/TestBase.java
@@ -35,6 +35,7 @@ import 
org.apache.sysds.test.component.compress.TestConstants.ValueRange;
 import org.apache.sysds.test.component.compress.TestConstants.ValueType;
 
 public class TestBase {
+       // private static final Log LOG = 
LogFactory.getLog(TestBase.class.getName());
 
        protected ValueType valType;
        protected ValueRange valRange;
@@ -70,20 +71,23 @@ public class TestBase {
                                        this.min = this.max;
                                        // Do not Break, utilize the RAND 
afterwards.
                                case RAND:
-                                       this.input = 
TestUtils.generateTestMatrix(rows, cols, min, max, sparsity, 7);
+                                       this.input = 
TestUtils.generateTestMatrix(rows, cols, min, max, sparsity, seed);
                                        break;
                                case RAND_ROUND:
-                                       this.input = 
TestUtils.round(TestUtils.generateTestMatrix(rows, cols, min, max, sparsity, 
7));
+                                       this.input = 
TestUtils.round(TestUtils.generateTestMatrix(rows, cols, min, max, sparsity, 
seed));
                                        break;
                                case OLE_COMPRESSIBLE:
                                        // Note the Compressible Input 
generator, generates an already Transposed input
                                        // normally, therefore last argument is 
true, to build a non transposed matrix.
                                        this.input = 
CompressibleInputGenerator.getInputDoubleMatrix(rows, cols, CompressionType.OLE,
-                                               (max - min), max, min, 
sparsity, 7, true);
+                                               (max - min), max, min, 
sparsity, seed, true);
                                        break;
                                case RLE_COMPRESSIBLE:
                                        this.input = 
CompressibleInputGenerator.getInputDoubleMatrix(rows, cols, CompressionType.RLE,
-                                               (max - min), max, min, 
sparsity, 7, true);
+                                               (max - min), max, min, 
sparsity, seed, true);
+                                       break;
+                               case ONE_HOT_ENCODED:
+                                       this.input = 
CompressibleInputGenerator.getInputOneHotMatrix(rows, cols, seed);
                                        break;
                                default:
                                        throw new NotImplementedException("Not 
Implemented Test Value type input generator");
@@ -94,6 +98,7 @@ public class TestBase {
                        this.compressionSettings = compressionSettings.create();
 
                        mb = DataConverter.convertToMatrixBlock(this.input);
+
                }
                catch(Exception e) {
                        e.printStackTrace();
diff --git 
a/src/test/java/org/apache/sysds/test/component/compress/TestConstants.java 
b/src/test/java/org/apache/sysds/test/component/compress/TestConstants.java
index c936c1b..649e96c 100644
--- a/src/test/java/org/apache/sysds/test/component/compress/TestConstants.java
+++ b/src/test/java/org/apache/sysds/test/component/compress/TestConstants.java
@@ -38,6 +38,7 @@ public class TestConstants {
                RAND_ROUND, // Values rounded to nearest whole numbers.
                OLE_COMPRESSIBLE, // Ideal inputs for OLE Compression.
                RLE_COMPRESSIBLE, // Ideal inputs for RLE Compression.
+               ONE_HOT_ENCODED,
        }
 
        public enum MatrixTypology {
diff --git 
a/src/test/java/org/apache/sysds/test/component/compress/colgroup/JolEstimateTest.java
 
b/src/test/java/org/apache/sysds/test/component/compress/colgroup/JolEstimateTest.java
index c32ccbe..b370451 100644
--- 
a/src/test/java/org/apache/sysds/test/component/compress/colgroup/JolEstimateTest.java
+++ 
b/src/test/java/org/apache/sysds/test/component/compress/colgroup/JolEstimateTest.java
@@ -58,7 +58,7 @@ public abstract class JolEstimateTest {
        public abstract CompressionType getCT();
 
        private final long actualSize;
-       // The actual compressed column group
+       private final int actualNumberUnique;
        private final AColGroup cg;
 
        public JolEstimateTest(MatrixBlock mbt) {
@@ -72,8 +72,9 @@ public abstract class JolEstimateTest {
                                
.setValidCompressions(EnumSet.of(getCT())).create();
                        cs.transposed = true;
                        ABitmap ubm = BitmapEncoder.extractBitmap(colIndexes, 
mbt, true);
-                       cg = ColGroupFactory.compress(colIndexes, 
mbt.getNumColumns(), ubm, getCT(), cs, mbt);
+                       cg = ColGroupFactory.compress(colIndexes, 
mbt.getNumColumns(), ubm, getCT(), cs, mbt, 1);
                        actualSize = cg.estimateInMemorySize();
+                       actualNumberUnique = cg.getNumValues();
                }
                catch(Exception e) {
                        e.printStackTrace();
@@ -83,21 +84,7 @@ public abstract class JolEstimateTest {
 
        @Test
        public void compressedSizeInfoEstimatorExact() {
-               try {
-                       CompressionSettings cs = new 
CompressionSettingsBuilder().setSamplingRatio(1.0)
-                               
.setValidCompressions(EnumSet.of(getCT())).setSeed(seed).create();
-                       cs.transposed = true;
-
-                       final long estimateCSI = 
CompressedSizeEstimatorFactory.getSizeEstimator(mbt, cs)
-                               
.estimateCompressedColGroupSize().getCompressionSize(cg.getCompType());
-
-                       boolean res = Math.abs(estimateCSI - actualSize) <= 0;
-                       assertTrue("CSI estimate " + estimateCSI + " should be 
exactly " + actualSize + "\n" + cg.toString(), res);
-               }
-               catch(Exception e) {
-                       e.printStackTrace();
-                       assertTrue("Failed exact test " + getCT(), false);
-               }
+               compressedSizeInfoEstimatorSample(1.0, 1.0);
        }
 
        @Test
@@ -107,48 +94,59 @@ public abstract class JolEstimateTest {
 
        @Test
        public void compressedSizeInfoEstimatorSample_50() {
-               compressedSizeInfoEstimatorSample(0.5, 0.90);
+               compressedSizeInfoEstimatorSample(0.5, 0.8);
        }
 
        @Test
        public void compressedSizeInfoEstimatorSample_20() {
-               compressedSizeInfoEstimatorSample(0.2, 0.8);
+               compressedSizeInfoEstimatorSample(0.2, 0.7);
        }
 
-       @Test
-       public void compressedSizeInfoEstimatorSample_10() {
-               compressedSizeInfoEstimatorSample(0.1, 0.75);
-       }
+       // @Test
+       // public void compressedSizeInfoEstimatorSample_10() {
+       //      compressedSizeInfoEstimatorSample(0.1, 0.6);
+       // }
 
-       @Test
-       public void compressedSizeInfoEstimatorSample_5() {
-               compressedSizeInfoEstimatorSample(0.05, 0.7);
-       }
+       // @Test
+       // public void compressedSizeInfoEstimatorSample_5() {
+       //      compressedSizeInfoEstimatorSample(0.05, 0.5);
+       // }
 
-       @Test
-       public void compressedSizeInfoEstimatorSample_1() {
-               compressedSizeInfoEstimatorSample(0.01, 0.6);
-       }
+       // @Test
+       // public void compressedSizeInfoEstimatorSample_1() {
+       //      compressedSizeInfoEstimatorSample(0.01, 0.4);
+       // }
 
        public void compressedSizeInfoEstimatorSample(double ratio, double 
tolerance) {
                try {
-                       if(mbt.getNumColumns() < 
CompressedSizeEstimatorFactory.minimumSampleSize)
-                               return; // Skip the tests that anyway wouldn't 
use the sample based approach.
 
                        CompressionSettings cs = new 
CompressionSettingsBuilder().setSamplingRatio(ratio)
-                               
.setValidCompressions(EnumSet.of(getCT())).setSeed(seed).create();
+                               
.setValidCompressions(EnumSet.of(getCT())).setMinimumSampleSize(100).setSeed(seed).create();
                        cs.transposed = true;
 
                        final CompressedSizeInfoColGroup cgsi = 
CompressedSizeEstimatorFactory.getSizeEstimator(mbt, cs)
                                .estimateCompressedColGroupSize();
+
+                       if(cg.getCompType() != CompressionType.UNCOMPRESSED && 
actualNumberUnique > 10) {
+
+                               final int estimateNUniques = cgsi.getNumVals();
+                               final double minToleranceNUniques = 
actualNumberUnique * tolerance;
+                               final double maxToleranceNUniques = 
actualNumberUnique / tolerance;
+                               final String uniqueString = 
minToleranceNUniques + " < " + estimateNUniques + " < "
+                                       + maxToleranceNUniques;
+                               final boolean withinToleranceOnNUniques = 
minToleranceNUniques <= actualNumberUnique &&
+                                       actualNumberUnique <= 
maxToleranceNUniques;
+                               assertTrue("CSI Sampled estimate of number of 
unique values not in range " + uniqueString + "\n" + cgsi,
+                                       withinToleranceOnNUniques);
+                       }
+
                        final long estimateCSI = 
cgsi.getCompressionSize(cg.getCompType());
                        final double minTolerance = actualSize * tolerance;
                        final double maxTolerance = actualSize / tolerance;
                        final String rangeString = minTolerance + " < " + 
estimateCSI + " < " + maxTolerance;
-                       boolean res = minTolerance < estimateCSI && estimateCSI 
< maxTolerance;
-                       assertTrue(
-                               "CSI Sampled estimate is not in tolerance range 
" + rangeString + "\n" + cgsi + "\n" + cg.toString(),
-                               res);
+                       final boolean withinToleranceOnSize = minTolerance <= 
estimateCSI && estimateCSI <= maxTolerance;
+                       assertTrue("CSI Sampled estimate is not in tolerance 
range " + rangeString + " Actual number uniques:"
+                               + actualNumberUnique + "\n" + cgsi, 
withinToleranceOnSize);
 
                }
                catch(Exception e) {
diff --git 
a/src/test/java/org/apache/sysds/test/component/compress/estim/SampleEstimatorTest.java
 
b/src/test/java/org/apache/sysds/test/component/compress/estim/SampleEstimatorTest.java
new file mode 100644
index 0000000..fba1088
--- /dev/null
+++ 
b/src/test/java/org/apache/sysds/test/component/compress/estim/SampleEstimatorTest.java
@@ -0,0 +1,119 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one
+ * or more contributor license agreements.  See the NOTICE file
+ * distributed with this work for additional information
+ * regarding copyright ownership.  The ASF licenses this file
+ * to you under the Apache License, Version 2.0 (the
+ * "License"); you may not use this file except in compliance
+ * with the License.  You may obtain a copy of the License at
+ *
+ *   http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing,
+ * software distributed under the License is distributed on an
+ * "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+ * KIND, either express or implied.  See the License for the
+ * specific language governing permissions and limitations
+ * under the License.
+ */
+
+package org.apache.sysds.test.component.compress.estim;
+
+import static org.junit.Assert.assertTrue;
+
+import org.apache.commons.logging.Log;
+import org.apache.commons.logging.LogFactory;
+import org.apache.sysds.runtime.compress.CompressionSettings;
+import org.apache.sysds.runtime.compress.CompressionSettingsBuilder;
+import org.apache.sysds.runtime.compress.estim.CompressedSizeEstimator;
+import org.apache.sysds.runtime.compress.estim.CompressedSizeEstimatorFactory;
+import org.apache.sysds.runtime.matrix.data.MatrixBlock;
+import org.apache.sysds.runtime.util.DataConverter;
+import org.apache.sysds.test.TestUtils;
+import org.junit.Test;
+
+public class SampleEstimatorTest {
+
+       protected static final Log LOG = 
LogFactory.getLog(SampleEstimatorTest.class.getName());
+
+       private static final int seed = 1512314;
+
+       final MatrixBlock mbt;
+
+       public SampleEstimatorTest() {
+               // matrix block 2 columns
+               mbt = DataConverter
+                       
.convertToMatrixBlock(TestUtils.round(TestUtils.generateTestMatrix(2, 500000, 
0, 299, 1.0, seed + 1)));
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorFull() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(1.0, 1.0);
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorSample_90() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(0.9, 0.9);
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorSample_50() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(0.5, 0.90);
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorSample_20() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(0.2, 0.8);
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorSample_10() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(0.1, 0.75);
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorSample_5() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(0.05, 0.7);
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorSample_1() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(0.01, 0.6);
+       }
+
+       @Test
+       public void compressedSizeInfoEstimatorSample_p1() {
+               
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(0.001, 0.5);
+       }
+
+       /**
+        * This test verify that the estimated number or unique values in 
individual columns is adhered to when analyzing
+        * multi columns.
+        * 
+        * The important part here is not if the number of unique elements is 
estimated correctly, but that the relation
+        * between observations is preserved.
+        * 
+        * @param ratio     Ratio to sample
+        * @param tolerance A percentage tolerance in number of unique element 
estimated
+        */
+       private void 
testSampleEstimateIsAtMaxEstimatedElementsInEachColumnsProduct(double ratio, 
double tolerance) {
+
+               final CompressionSettings cs_estimate = new 
CompressionSettingsBuilder().setMinimumSampleSize(100)
+                       .setSamplingRatio(ratio).setSeed(seed).create();
+
+               cs_estimate.transposed = true;
+
+               final CompressedSizeEstimator estimate = 
CompressedSizeEstimatorFactory.getSizeEstimator(mbt, cs_estimate);
+               final int estimate_1 = 
estimate.estimateCompressedColGroupSize(new int[] {0}).getNumVals() + 1;
+               final int estimate_2 = 
estimate.estimateCompressedColGroupSize(new int[] {1}).getNumVals() + 1;
+
+               final int estimate_full = 
estimate.estimateCompressedColGroupSize(new int[] {0, 1}, estimate_1 * 
estimate_2)
+                       .getNumVals();
+               assertTrue(
+                       "Estimate of all columns should be upper bounded by 
distinct of each column multiplied: " + estimate_full
+                               + " * " + tolerance + " <= " + estimate_1 * 
estimate_2,
+                       estimate_full * tolerance <= estimate_1 * estimate_2);
+
+       }
+
+}

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