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+<!DOCTYPE html>
+<!-- Start _layouts/doc_page.html-->
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+ <div class="navbar-collapse collapse">
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+<!-- End _include/nav_bar.html -->
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+ <h4>API Snapshots:
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+ <a href="/api/pig/snapshot/apidocs/index.html">Pig</a>,
+ <a href="/api/hive/snapshot/apidocs/index.html">Hive</a>,
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+<link rel="stylesheet" href="/css/toc.css">
+<div id="toc" class="nav toc hidden-print">
+
+ <p id="background">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_background">Background</a>
+ </p>
+ <div class="collapse" id="collapse_background">
+ <li><a href="/docs/Background/TheChallenge.html">•The Challenge</a></li>
+ <li><a href="/docs/Background/SketchOrigins.html">•Sketch Origins</a></li>
+ <li><a href="/docs/Background/SketchElements.html">•Sketch
Elements</a></li>
+ <li><a href="/docs/Background/Presentations.html">•Presentations</a></li>
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/DataSketches_deck.pdf";>•Overview
Slide Deck</a></li>
+ </div>
+
+ <p id="architecture-and-design">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_architecture_and_design">Architecture And Design</a>
+ </p>
+ <div class="collapse" id="collapse_architecture_and_design">
+ <li><a href="/docs/Architecture/MajorSketchFamilies.html">•The Major
Sketch Families</a></li>
+ <li><a href="/docs/Architecture/LargeScale.html">•Large Scale
Computing</a></li>
+ <li><a href="/docs/Architecture/KeyFeatures.html">•Key Features</a></li>
+ <li><a href="/docs/Architecture/SketchFeaturesMatrix.html">•Sketch
Features Matrix</a></li>
+ <li><a href="/docs/Architecture/Components.html">•Components</a></li>
+ <li><a href="/docs/Architecture/SketchesByComponent.html">•Sketches by
Component</a></li>
+ <li><a href="/docs/Architecture/SketchCriteria.html">•Sketch
Criteria</a></li>
+
+ <p id="memory-package">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_memory_package">Memory Package</a>
+ </p>
+ <div class="collapse" id="collapse_memory_package">
+ <li><a href="/docs/Memory/MemoryPackage.html">•Memory Package</a></li>
+ <li><a href="/docs/Memory/MemoryPerformance.html">•Memory Package
Performance</a></li>
+ </div>
+ <li><a href="/docs/Architecture/OrderSensitivity.html">•Notes on Order
Sensitivity</a></li>
+ <li><a href="/docs/Architecture/Concurrency.html">•Notes on
Concurrency</a></li>
+ </div>
+
+ <p id="sketch-families">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_sketch_families">Sketch Families</a>
+ </p>
+ <div class="collapse" id="collapse_sketch_families">
+
+ <p id="distinct-counting">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_distinct_counting">Distinct Counting</a>
+ </p>
+ <div class="collapse" id="collapse_distinct_counting">
+ <li><a href="/docs/DistinctCountFeaturesMatrix.html">•Features
Matrix</a></li>
+ <li><a href="/docs/DistinctCountMeritComparisons.html">•Figures-of-Merit
Comparison</a></li>
+
+ <p id="cpc-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_cpc_sketches">CPC Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_cpc_sketches">
+ <li><a href="/docs/CPC/CPC.html">•CPC Sketch</a></li>
+ <li><a href="/docs/CPC/CpcPerformance.html">•CPC Sketch
Performance</a></li>
+
+ <p id="cpc-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_cpc_examples">CPC Examples</a>
+ </p>
+ <div class="collapse" id="collapse_cpc_examples">
+ <li><a href="/docs/CPC/CpcJavaExample.html">•CPC Sketch Java
Example</a></li>
+ <li><a href="/docs/CPC/CpcCppExample.html">•CPC Sketch C++
Example</a></li>
+ <li><a href="/docs/CPC/CpcPigExample.html">•CPC Sketch Pig
UDFs</a></li>
+ <li><a href="/docs/CPC/CpcHiveExample.html">•CPC Sketch Hive
UDFs</a></li>
+ </div>
+ </div>
+
+ <p id="hyperloglog-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_hyperloglog_sketches">HyperLogLog Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_hyperloglog_sketches">
+ <li><a href="/docs/HLL/HLL.html">•HLL Sketch</a></li>
+ <li><a href="/docs/HLL/HllMap.html">•HLL Map Sketch</a></li>
+
+ <p id="hll-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_hll_examples">HLL Examples</a>
+ </p>
+ <div class="collapse" id="collapse_hll_examples">
+ <li><a href="/docs/HLL/HllJavaExample.html">•HLL Sketch Java
Example</a></li>
+ <li><a href="/docs/HLL/HllCppExample.html">•HLL Sketch C++
Example</a></li>
+ <li><a href="/docs/HLL/HllPigUDFs.html">•HLL Sketch Pig UDFs</a></li>
+ <li><a href="/docs/HLL/HllHiveUDFs.html">•HLL Sketch Hive
UDFs</a></li>
+ </div>
+
+ <p id="hll-studies">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_hll_studies">HLL Studies</a>
+ </p>
+ <div class="collapse" id="collapse_hll_studies">
+ <li><a href="/docs/HLL/HllPerformance.html">•HLL Sketch
Performance</a></li>
+ <li><a href="/docs/HLL/Hll_vs_CS_Hllpp.html">•HLL vs Clearspring
HLL++</a></li>
+ <li><a
href="/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html">•HLL Sketch vs Druid
HyperLogLogCollector</a></li>
+ </div>
+ </div>
+
+ <p id="theta-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_theta_sketches">Theta Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_theta_sketches">
+ <li><a href="/docs/Theta/ThetaSketchFramework.html">•Theta Sketch
Framework</a></li>
+
+ <p id="theta-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_theta_examples">Theta Examples</a>
+ </p>
+ <div class="collapse" id="collapse_theta_examples">
+ <li><a href="/docs/Theta/ConcurrentThetaSketch.html">•Concurrent
Theta Sketch</a></li>
+ <li><a href="/docs/Theta/ThetaJavaExample.html">•Theta Sketch Java
Example</a></li>
+ <li><a href="/docs/Theta/ThetaSparkExample.html">•Theta Sketch Spark
Example</a></li>
+ <li><a href="/docs/Theta/ThetaPigUDFs.html">•Theta Sketch Pig
UDFs</a></li>
+ <li><a href="/docs/Theta/ThetaHiveUDFs.html">•Theta Sketch Hive
UDFs</a></li>
+ </div>
+
+ <p id="kmv-tutorial">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_kmv_tutorial">KMV Tutorial</a>
+ </p>
+ <div class="collapse" id="collapse_kmv_tutorial">
+ <li><a href="/docs/Theta/InverseEstimate.html">•The Inverse
Estimate</a></li>
+ <li><a href="/docs/Theta/KMVempty.html">•Empty Sketch</a></li>
+ <li><a href="/docs/Theta/KMVfirstEst.html">•First Estimator</a></li>
+ <li><a href="/docs/Theta/KMVbetterEst.html">•Better
Estimator</a></li>
+ <li><a href="/docs/Theta/KMVrejection.html">•Rejection Rules</a></li>
+ <li><a href="/docs/Theta/KMVupdateVkth.html">•Update V(kth)
Rule</a></li>
+ </div>
+
+ <p id="set-operations-and-p-sampling">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_set_operations_and_p-sampling">Set Operations and P-sampling</a>
+ </p>
+ <div class="collapse" id="collapse_set_operations_and_p-sampling">
+ <li><a href="/docs/Theta/ThetaSketchSetOps.html">•Set
Operations</a></li>
+ <li><a
href="/docs/Theta/ThetaPSampling.html">•<i>p</i>-Sampling</a></li>
+ </div>
+
+ <p id="accuracy">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_accuracy">Accuracy</a>
+ </p>
+ <div class="collapse" id="collapse_accuracy">
+ <li><a href="/docs/Theta/ThetaAccuracy.html">•Basic Accuracy</a></li>
+ <li><a href="/docs/Theta/ThetaAccuracyPlots.html">•Accuracy
Plots</a></li>
+ <li><a href="/docs/Theta/ThetaErrorTable.html">•Relative Error
Table</a></li>
+ <li><a href="/docs/Theta/ThetaSketchSetOpsAccuracy.html">•SetOp
Accuracy</a></li>
+ <li><a href="/docs/Theta/AccuracyOfDifferentKUnions.html">•Unions
With Different k</a></li>
+ </div>
+
+ <p id="size">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_size">Size</a>
+ </p>
+ <div class="collapse" id="collapse_size">
+ <li><a href="/docs/Theta/ThetaSize.html">•Theta Sketch Size</a></li>
+ </div>
+
+ <p id="speed">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_speed">Speed</a>
+ </p>
+ <div class="collapse" id="collapse_speed">
+ <li><a href="/docs/Theta/ThetaUpdateSpeed.html">•Update
Speed</a></li>
+ <li><a href="/docs/Theta/ThetaMergeSpeed.html">•Merge Speed</a></li>
+ </div>
+
+ <p id="theta-sketch-theory">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_theta_sketch_theory">Theta Sketch Theory</a>
+ </p>
+ <div class="collapse" id="collapse_theta_sketch_theory">
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/ThetaSketchFramework.pdf";>•Theta
Sketch Framework (PDF)</a></li>
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/SketchEquations.pdf";>•Sketch
Equations (PDF)</a></li>
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/DataSketches.pdf";>•DataSketches
(PDF)</a></li>
+ <li><a href="/docs/Theta/ThetaConfidenceIntervals.html">•Confidence
Intervals Notes</a></li>
+ <li><a href="/docs/Theta/ThetaMergingAlgorithm.html">•Merging
Algorithm Notes</a></li>
+ <li><a href="/docs/Theta/ThetaReferences.html">•Theta
References</a></li>
+ </div>
+ </div>
+
+ <p id="tuple-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_tuple_sketches">Tuple Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_tuple_sketches">
+ <li><a href="/docs/Tuple/TupleOverview.html">•Tuple Overview</a></li>
+
+ <p id="tuple-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_tuple_examples">Tuple Examples</a>
+ </p>
+ <div class="collapse" id="collapse_tuple_examples">
+ <li><a href="/docs/Tuple/TupleJavaExample.html">•Tuple Java
Example</a></li>
+ <li><a href="/docs/Tuple/TupleEngagementExample.html">•Tuple
Engagement Example</a></li>
+ <li><a href="/docs/Tuple/TuplePigUDFs.html">•Tuple Pig UDFs</a></li>
+ <li><a href="/docs/Tuple/TupleHiveUDFs.html">•Tuple Hive
UDFs</a></li>
+ </div>
+ </div>
+ </div>
+
+ <p id="most-frequent">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_most_frequent">Most Frequent</a>
+ </p>
+ <div class="collapse" id="collapse_most_frequent">
+ <li><a href="/docs/Frequency/FrequencySketchesOverview.html">•Frequency
Sketches Overview</a></li>
+
+ <p id="frequent-item-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_frequent_item_sketches">Frequent Item Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_frequent_item_sketches">
+ <li><a href="/docs/Frequency/FrequentItemsOverview.html">•Frequent
Items Overview</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsErrorTable.html">•Frequent
Items Error Table</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsReferences.html">•Frequent
Items References</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsPerformance.html">•Frequent
Items Performance</a></li>
+
+ <p id="most-frequent-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_most_frequent_examples">Most Frequent Examples</a>
+ </p>
+ <div class="collapse" id="collapse_most_frequent_examples">
+ <li><a
href="/docs/Frequency/FrequentItemsJavaExample.html">•Frequent Items Java
Example</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsCppExample.html">•Frequent
Items C++ Example</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsPigUDFs.html">•Frequent
Items Pig UDFs</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsHiveUDFs.html">•Frequent
Items Hive UDFs</a></li>
+ </div>
+ </div>
+
+ <p id="frequent-distinct-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_frequent_distinct_sketches">Frequent Distinct Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_frequent_distinct_sketches">
+ <li><a
href="/docs/Frequency/FrequentDistinctTuplesSketch.html">•Frequent Distinct
Tuples Sketch</a></li>
+ </div>
+ </div>
+
+ <p id="quantiles-and-histograms">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_and_histograms">
+ <li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
+ <li><a href="/docs/Quantiles/QuantilesAccuracy.html">•Quantiles Accuracy
and Size</a></li>
+
+ <p id="quantiles-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_examples">Quantiles Examples</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_examples">
+ <li><a href="/docs/Quantiles/QuantilesJavaExample.html">•Quantiles
Sketch Java Example</a></li>
+ <li><a href="/docs/Quantiles/QuantilesCppExample.html">•KLL Quantiles
Sketch C++ Example</a></li>
+ <li><a href="/docs/Quantiles/QuantilesPigUDFs.html">•Quantiles Sketch
Pig UDFs</a></li>
+ <li><a href="/docs/Quantiles/QuantilesHiveUDFs.html">•Quantiles Sketch
Hive UDFs</a></li>
+ </div>
+
+ <p id="quantiles-studies">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_studies">Quantiles Studies</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_studies">
+ <li><a href="/docs/Quantiles/Definitions.html">•Definitions for
Quantiles Studies</a></li>
+ <li><a href="/docs/Quantiles/KLLSketch.html">•New KLL sketch and
comparison with DoublesSketch</a></li>
+ <li><a href="/docs/Quantiles/KllSketchVsTDigest.html">•KLL sketch vs
t-digest</a></li>
+ <li><a href="/docs/Quantiles/DruidApproxHistogramStudy.html">•Druid
Approximate Histogram</a></li>
+ <li><a href="/docs/Quantiles/MomentsSketchStudy.html">•Moments Sketch
Study</a></li>
+ <li><a href="/docs/Quantiles/QuantilesStreamAStudy.html">•Quantiles
StreamA Study</a></li>
+ <li><a href="/docs/Quantiles/ExactQuantiles.html">•Exact Quantiles for
Studies</a></li>
+ </div>
+
+ <p id="quantiles-sketch-theory">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_sketch_theory">Quantiles Sketch Theory</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_sketch_theory">
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/Quantiles_KLL.pdf";>•Optimal
Quantile Approximation in Streams</a></li>
+ <li><a href="/docs/Quantiles/QuantilesReferences.html">•Quantiles
References</a></li>
+ </div>
+ </div>
+
+ <p id="sampling">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_sampling">Sampling</a>
+ </p>
+ <div class="collapse" id="collapse_sampling">
+ <li><a href="/docs/Sampling/ReservoirSampling.html">•Reservoir
Sampling</a></li>
+ <li><a
href="/docs/Sampling/ReservoirSamplingPerformance.html">•Reservoir Sampling
Performance</a></li>
+ <li><a href="/docs/Sampling/VarOptSampling.html">•VarOpt
Sampling</a></li>
+
+ <p id="sampling-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_sampling_examples">Sampling Examples</a>
+ </p>
+ <div class="collapse" id="collapse_sampling_examples">
+ <li><a href="/docs/Sampling/ReservoirSamplingJava.html">•Reservoir
Sampling Java Example</a></li>
+ <li><a href="/docs/Sampling/ReservoirSamplingPigUDFs.html">•Reservoir
Sampling Pig UDFs</a></li>
+ <li><a href="/docs/Sampling/VarOptSamplingJava.html">•VarOpt Sampling
Java Example</a></li>
+ <li><a href="/docs/Sampling/VarOptPigUDFs.html">•VarOpt Sampling Pig
UDFs</a></li>
+ </div>
+ </div>
+ </div>
+
+ <p id="system-integrations">
+ <a data-toggle="collapse" class="menu collapsed"
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+ <li><a href="/docs/SystemIntegrations/ApacheDruidIntegration.html">•Using
Sketches in ApacheDruid</a></li>
+ <li><a href="/docs/SystemIntegrations/ApacheHiveIntegration.html">•Using
Sketches in Apache Hive</a></li>
+ <li><a href="/docs/SystemIntegrations/ApachePigIntegration.html">•Using
Sketches in Apache Pig</a></li>
+ <li><a href="/docs/SystemIntegrations/PostgreSQLIntegration.html">•Using
Sketches in PostgreSQL</a></li>
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href="#collapse_community">Community</a>
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+ <li><a href="/docs/Community/Transitioning.html">•Transitioning from prior
GitHub Site</a></li>
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+ <a data-toggle="collapse" class="menu collapsed"
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+<h1 id="reqsketch-accuracy-with-adversarial-streams">ReqSketch Accuracy with
Adversarial Streams</h1>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T12_LT_Sh.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T12_LT_NoSh.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T0_LT_Sorted.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T0_LT_Reversed.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T0_LT_Random.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T0_LT_Zoomin.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T0_LT_Zoomout.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T0_LT_Sqrt.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T0_LT_FlipFlop.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
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Foundation</a>,
+ Licensed under the Apache License, Version 2.0. All Rights
Reserved.<br/>
+ Apache DataSketches, Apache, the Apache feather logo, and the Apache
DataSketches project logos are trademarks of The Apache Software
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+ All other marks mentioned may be trademarks or registered trademarks
of their respective owners.<br/>
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+ <b>Disclaimer:</b> Apache DataSketches is an effort undergoing
incubation at The Apache Software Foundation (ASF), sponsored by the Apache
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further review indicates that the infrastructure, communications, and decision
making process have stabilized in a manner consistent with other successful ASF
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diff --git a/output/docs/REQ/ReqAccuracyRandomShuffled.html
b/output/docs/REQ/ReqAccuracyRandomShuffled.html
new file mode 100644
index 0000000..837db39
--- /dev/null
+++ b/output/docs/REQ/ReqAccuracyRandomShuffled.html
@@ -0,0 +1,626 @@
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+<!-- Start _layouts/doc_page.html-->
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+<div id="toc" class="nav toc hidden-print">
+
+ <p id="background">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_background">Background</a>
+ </p>
+ <div class="collapse" id="collapse_background">
+ <li><a href="/docs/Background/TheChallenge.html">•The Challenge</a></li>
+ <li><a href="/docs/Background/SketchOrigins.html">•Sketch Origins</a></li>
+ <li><a href="/docs/Background/SketchElements.html">•Sketch
Elements</a></li>
+ <li><a href="/docs/Background/Presentations.html">•Presentations</a></li>
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/DataSketches_deck.pdf";>•Overview
Slide Deck</a></li>
+ </div>
+
+ <p id="architecture-and-design">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_architecture_and_design">Architecture And Design</a>
+ </p>
+ <div class="collapse" id="collapse_architecture_and_design">
+ <li><a href="/docs/Architecture/MajorSketchFamilies.html">•The Major
Sketch Families</a></li>
+ <li><a href="/docs/Architecture/LargeScale.html">•Large Scale
Computing</a></li>
+ <li><a href="/docs/Architecture/KeyFeatures.html">•Key Features</a></li>
+ <li><a href="/docs/Architecture/SketchFeaturesMatrix.html">•Sketch
Features Matrix</a></li>
+ <li><a href="/docs/Architecture/Components.html">•Components</a></li>
+ <li><a href="/docs/Architecture/SketchesByComponent.html">•Sketches by
Component</a></li>
+ <li><a href="/docs/Architecture/SketchCriteria.html">•Sketch
Criteria</a></li>
+
+ <p id="memory-package">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_memory_package">Memory Package</a>
+ </p>
+ <div class="collapse" id="collapse_memory_package">
+ <li><a href="/docs/Memory/MemoryPackage.html">•Memory Package</a></li>
+ <li><a href="/docs/Memory/MemoryPerformance.html">•Memory Package
Performance</a></li>
+ </div>
+ <li><a href="/docs/Architecture/OrderSensitivity.html">•Notes on Order
Sensitivity</a></li>
+ <li><a href="/docs/Architecture/Concurrency.html">•Notes on
Concurrency</a></li>
+ </div>
+
+ <p id="sketch-families">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_sketch_families">Sketch Families</a>
+ </p>
+ <div class="collapse" id="collapse_sketch_families">
+
+ <p id="distinct-counting">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_distinct_counting">Distinct Counting</a>
+ </p>
+ <div class="collapse" id="collapse_distinct_counting">
+ <li><a href="/docs/DistinctCountFeaturesMatrix.html">•Features
Matrix</a></li>
+ <li><a href="/docs/DistinctCountMeritComparisons.html">•Figures-of-Merit
Comparison</a></li>
+
+ <p id="cpc-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_cpc_sketches">CPC Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_cpc_sketches">
+ <li><a href="/docs/CPC/CPC.html">•CPC Sketch</a></li>
+ <li><a href="/docs/CPC/CpcPerformance.html">•CPC Sketch
Performance</a></li>
+
+ <p id="cpc-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_cpc_examples">CPC Examples</a>
+ </p>
+ <div class="collapse" id="collapse_cpc_examples">
+ <li><a href="/docs/CPC/CpcJavaExample.html">•CPC Sketch Java
Example</a></li>
+ <li><a href="/docs/CPC/CpcCppExample.html">•CPC Sketch C++
Example</a></li>
+ <li><a href="/docs/CPC/CpcPigExample.html">•CPC Sketch Pig
UDFs</a></li>
+ <li><a href="/docs/CPC/CpcHiveExample.html">•CPC Sketch Hive
UDFs</a></li>
+ </div>
+ </div>
+
+ <p id="hyperloglog-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_hyperloglog_sketches">HyperLogLog Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_hyperloglog_sketches">
+ <li><a href="/docs/HLL/HLL.html">•HLL Sketch</a></li>
+ <li><a href="/docs/HLL/HllMap.html">•HLL Map Sketch</a></li>
+
+ <p id="hll-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_hll_examples">HLL Examples</a>
+ </p>
+ <div class="collapse" id="collapse_hll_examples">
+ <li><a href="/docs/HLL/HllJavaExample.html">•HLL Sketch Java
Example</a></li>
+ <li><a href="/docs/HLL/HllCppExample.html">•HLL Sketch C++
Example</a></li>
+ <li><a href="/docs/HLL/HllPigUDFs.html">•HLL Sketch Pig UDFs</a></li>
+ <li><a href="/docs/HLL/HllHiveUDFs.html">•HLL Sketch Hive
UDFs</a></li>
+ </div>
+
+ <p id="hll-studies">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_hll_studies">HLL Studies</a>
+ </p>
+ <div class="collapse" id="collapse_hll_studies">
+ <li><a href="/docs/HLL/HllPerformance.html">•HLL Sketch
Performance</a></li>
+ <li><a href="/docs/HLL/Hll_vs_CS_Hllpp.html">•HLL vs Clearspring
HLL++</a></li>
+ <li><a
href="/docs/HLL/HllSketchVsDruidHyperLogLogCollector.html">•HLL Sketch vs Druid
HyperLogLogCollector</a></li>
+ </div>
+ </div>
+
+ <p id="theta-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_theta_sketches">Theta Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_theta_sketches">
+ <li><a href="/docs/Theta/ThetaSketchFramework.html">•Theta Sketch
Framework</a></li>
+
+ <p id="theta-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_theta_examples">Theta Examples</a>
+ </p>
+ <div class="collapse" id="collapse_theta_examples">
+ <li><a href="/docs/Theta/ConcurrentThetaSketch.html">•Concurrent
Theta Sketch</a></li>
+ <li><a href="/docs/Theta/ThetaJavaExample.html">•Theta Sketch Java
Example</a></li>
+ <li><a href="/docs/Theta/ThetaSparkExample.html">•Theta Sketch Spark
Example</a></li>
+ <li><a href="/docs/Theta/ThetaPigUDFs.html">•Theta Sketch Pig
UDFs</a></li>
+ <li><a href="/docs/Theta/ThetaHiveUDFs.html">•Theta Sketch Hive
UDFs</a></li>
+ </div>
+
+ <p id="kmv-tutorial">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_kmv_tutorial">KMV Tutorial</a>
+ </p>
+ <div class="collapse" id="collapse_kmv_tutorial">
+ <li><a href="/docs/Theta/InverseEstimate.html">•The Inverse
Estimate</a></li>
+ <li><a href="/docs/Theta/KMVempty.html">•Empty Sketch</a></li>
+ <li><a href="/docs/Theta/KMVfirstEst.html">•First Estimator</a></li>
+ <li><a href="/docs/Theta/KMVbetterEst.html">•Better
Estimator</a></li>
+ <li><a href="/docs/Theta/KMVrejection.html">•Rejection Rules</a></li>
+ <li><a href="/docs/Theta/KMVupdateVkth.html">•Update V(kth)
Rule</a></li>
+ </div>
+
+ <p id="set-operations-and-p-sampling">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_set_operations_and_p-sampling">Set Operations and P-sampling</a>
+ </p>
+ <div class="collapse" id="collapse_set_operations_and_p-sampling">
+ <li><a href="/docs/Theta/ThetaSketchSetOps.html">•Set
Operations</a></li>
+ <li><a
href="/docs/Theta/ThetaPSampling.html">•<i>p</i>-Sampling</a></li>
+ </div>
+
+ <p id="accuracy">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_accuracy">Accuracy</a>
+ </p>
+ <div class="collapse" id="collapse_accuracy">
+ <li><a href="/docs/Theta/ThetaAccuracy.html">•Basic Accuracy</a></li>
+ <li><a href="/docs/Theta/ThetaAccuracyPlots.html">•Accuracy
Plots</a></li>
+ <li><a href="/docs/Theta/ThetaErrorTable.html">•Relative Error
Table</a></li>
+ <li><a href="/docs/Theta/ThetaSketchSetOpsAccuracy.html">•SetOp
Accuracy</a></li>
+ <li><a href="/docs/Theta/AccuracyOfDifferentKUnions.html">•Unions
With Different k</a></li>
+ </div>
+
+ <p id="size">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_size">Size</a>
+ </p>
+ <div class="collapse" id="collapse_size">
+ <li><a href="/docs/Theta/ThetaSize.html">•Theta Sketch Size</a></li>
+ </div>
+
+ <p id="speed">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_speed">Speed</a>
+ </p>
+ <div class="collapse" id="collapse_speed">
+ <li><a href="/docs/Theta/ThetaUpdateSpeed.html">•Update
Speed</a></li>
+ <li><a href="/docs/Theta/ThetaMergeSpeed.html">•Merge Speed</a></li>
+ </div>
+
+ <p id="theta-sketch-theory">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_theta_sketch_theory">Theta Sketch Theory</a>
+ </p>
+ <div class="collapse" id="collapse_theta_sketch_theory">
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/ThetaSketchFramework.pdf";>•Theta
Sketch Framework (PDF)</a></li>
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/SketchEquations.pdf";>•Sketch
Equations (PDF)</a></li>
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/DataSketches.pdf";>•DataSketches
(PDF)</a></li>
+ <li><a href="/docs/Theta/ThetaConfidenceIntervals.html">•Confidence
Intervals Notes</a></li>
+ <li><a href="/docs/Theta/ThetaMergingAlgorithm.html">•Merging
Algorithm Notes</a></li>
+ <li><a href="/docs/Theta/ThetaReferences.html">•Theta
References</a></li>
+ </div>
+ </div>
+
+ <p id="tuple-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_tuple_sketches">Tuple Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_tuple_sketches">
+ <li><a href="/docs/Tuple/TupleOverview.html">•Tuple Overview</a></li>
+
+ <p id="tuple-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_tuple_examples">Tuple Examples</a>
+ </p>
+ <div class="collapse" id="collapse_tuple_examples">
+ <li><a href="/docs/Tuple/TupleJavaExample.html">•Tuple Java
Example</a></li>
+ <li><a href="/docs/Tuple/TupleEngagementExample.html">•Tuple
Engagement Example</a></li>
+ <li><a href="/docs/Tuple/TuplePigUDFs.html">•Tuple Pig UDFs</a></li>
+ <li><a href="/docs/Tuple/TupleHiveUDFs.html">•Tuple Hive
UDFs</a></li>
+ </div>
+ </div>
+ </div>
+
+ <p id="most-frequent">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_most_frequent">Most Frequent</a>
+ </p>
+ <div class="collapse" id="collapse_most_frequent">
+ <li><a href="/docs/Frequency/FrequencySketchesOverview.html">•Frequency
Sketches Overview</a></li>
+
+ <p id="frequent-item-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_frequent_item_sketches">Frequent Item Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_frequent_item_sketches">
+ <li><a href="/docs/Frequency/FrequentItemsOverview.html">•Frequent
Items Overview</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsErrorTable.html">•Frequent
Items Error Table</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsReferences.html">•Frequent
Items References</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsPerformance.html">•Frequent
Items Performance</a></li>
+
+ <p id="most-frequent-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_most_frequent_examples">Most Frequent Examples</a>
+ </p>
+ <div class="collapse" id="collapse_most_frequent_examples">
+ <li><a
href="/docs/Frequency/FrequentItemsJavaExample.html">•Frequent Items Java
Example</a></li>
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Items C++ Example</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsPigUDFs.html">•Frequent
Items Pig UDFs</a></li>
+ <li><a href="/docs/Frequency/FrequentItemsHiveUDFs.html">•Frequent
Items Hive UDFs</a></li>
+ </div>
+ </div>
+
+ <p id="frequent-distinct-sketches">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_frequent_distinct_sketches">Frequent Distinct Sketches</a>
+ </p>
+ <div class="collapse" id="collapse_frequent_distinct_sketches">
+ <li><a
href="/docs/Frequency/FrequentDistinctTuplesSketch.html">•Frequent Distinct
Tuples Sketch</a></li>
+ </div>
+ </div>
+
+ <p id="quantiles-and-histograms">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_and_histograms">
+ <li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles
Overview</a></li>
+ <li><a href="/docs/Quantiles/QuantilesAccuracy.html">•Quantiles Accuracy
and Size</a></li>
+
+ <p id="quantiles-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_examples">Quantiles Examples</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_examples">
+ <li><a href="/docs/Quantiles/QuantilesJavaExample.html">•Quantiles
Sketch Java Example</a></li>
+ <li><a href="/docs/Quantiles/QuantilesCppExample.html">•KLL Quantiles
Sketch C++ Example</a></li>
+ <li><a href="/docs/Quantiles/QuantilesPigUDFs.html">•Quantiles Sketch
Pig UDFs</a></li>
+ <li><a href="/docs/Quantiles/QuantilesHiveUDFs.html">•Quantiles Sketch
Hive UDFs</a></li>
+ </div>
+
+ <p id="quantiles-studies">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_studies">Quantiles Studies</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_studies">
+ <li><a href="/docs/Quantiles/Definitions.html">•Definitions for
Quantiles Studies</a></li>
+ <li><a href="/docs/Quantiles/KLLSketch.html">•New KLL sketch and
comparison with DoublesSketch</a></li>
+ <li><a href="/docs/Quantiles/KllSketchVsTDigest.html">•KLL sketch vs
t-digest</a></li>
+ <li><a href="/docs/Quantiles/DruidApproxHistogramStudy.html">•Druid
Approximate Histogram</a></li>
+ <li><a href="/docs/Quantiles/MomentsSketchStudy.html">•Moments Sketch
Study</a></li>
+ <li><a href="/docs/Quantiles/QuantilesStreamAStudy.html">•Quantiles
StreamA Study</a></li>
+ <li><a href="/docs/Quantiles/ExactQuantiles.html">•Exact Quantiles for
Studies</a></li>
+ </div>
+
+ <p id="quantiles-sketch-theory">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_quantiles_sketch_theory">Quantiles Sketch Theory</a>
+ </p>
+ <div class="collapse" id="collapse_quantiles_sketch_theory">
+ <li><a
href="https://github.com/apache/incubator-datasketches-website/tree/master/docs/pdf/Quantiles_KLL.pdf";>•Optimal
Quantile Approximation in Streams</a></li>
+ <li><a href="/docs/Quantiles/QuantilesReferences.html">•Quantiles
References</a></li>
+ </div>
+ </div>
+
+ <p id="sampling">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_sampling">Sampling</a>
+ </p>
+ <div class="collapse" id="collapse_sampling">
+ <li><a href="/docs/Sampling/ReservoirSampling.html">•Reservoir
Sampling</a></li>
+ <li><a
href="/docs/Sampling/ReservoirSamplingPerformance.html">•Reservoir Sampling
Performance</a></li>
+ <li><a href="/docs/Sampling/VarOptSampling.html">•VarOpt
Sampling</a></li>
+
+ <p id="sampling-examples">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_sampling_examples">Sampling Examples</a>
+ </p>
+ <div class="collapse" id="collapse_sampling_examples">
+ <li><a href="/docs/Sampling/ReservoirSamplingJava.html">•Reservoir
Sampling Java Example</a></li>
+ <li><a href="/docs/Sampling/ReservoirSamplingPigUDFs.html">•Reservoir
Sampling Pig UDFs</a></li>
+ <li><a href="/docs/Sampling/VarOptSamplingJava.html">•VarOpt Sampling
Java Example</a></li>
+ <li><a href="/docs/Sampling/VarOptPigUDFs.html">•VarOpt Sampling Pig
UDFs</a></li>
+ </div>
+ </div>
+ </div>
+
+ <p id="system-integrations">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_system_integrations">System Integrations</a>
+ </p>
+ <div class="collapse" id="collapse_system_integrations">
+ <li><a href="/docs/SystemIntegrations/ApacheDruidIntegration.html">•Using
Sketches in ApacheDruid</a></li>
+ <li><a href="/docs/SystemIntegrations/ApacheHiveIntegration.html">•Using
Sketches in Apache Hive</a></li>
+ <li><a href="/docs/SystemIntegrations/ApachePigIntegration.html">•Using
Sketches in Apache Pig</a></li>
+ <li><a href="/docs/SystemIntegrations/PostgreSQLIntegration.html">•Using
Sketches in PostgreSQL</a></li>
+ </div>
+
+ <p id="community">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_community">Community</a>
+ </p>
+ <div class="collapse" id="collapse_community">
+ <li><a href="/docs/Community/index.html">•Community</a></li>
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+ <li><a href="/docs/Community/Transitioning.html">•Transitioning from prior
GitHub Site</a></li>
+ <li><a href="/docs/Community/WhoUses.html">•Who Uses</a></li>
+ </div>
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+ <p id="research">
+ <a data-toggle="collapse" class="menu collapsed"
href="#collapse_research">Research</a>
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+ <div class="collapse" id="collapse_research">
+ <li><a href="/docs/Community/Research.html">•Research</a></li>
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+<h1 id="reqsketch-accuracy-with-random-shuffled-streams">ReqSketch Accuracy
with Random Shuffled Streams</h1>
+<p>This set of tests characterize the accuracy of the ReqSketch using random
shuffled streams.</p>
+<ul>
+ <li><a
href="https://github.com/apache/incubator-datasketches-characterization/blob/master/src/test/java/org/apache/datasketches/characterization/quantiles/ReqSketchAccuracyProfile.java";>Code</a>:
The code used to generate these characterization studies.</li>
+ <li><a
href="https://github.com/apache/incubator-datasketches-characterization/blob/master/src/main/resources/quantiles/ReqSketchAccuracyJob.conf";>Config</a>:
The human readable and editable configuration file that instructs the above
code with the specific properties used to run the test. These configuration
properties are different for each of the following plots and summarized below
with each plot.</li>
+</ul>
+
+<h2 id="test-design">Test Design</h2>
+<ul>
+ <li>Stream Length (SL): 2^20</li>
+ <li>Stream Values: Natural numbers, ℕ<sub>1</sub>, from 1 to SL, expressed
as 32-bit floats.</li>
+ <li>Y-axis: The absolute error of the sketch <em>getRank(value)</em>
method.</li>
+ <li>X-axis: The normalized rank [0.0, 1.0]</li>
+ <li>Plot Points (PP): 100. Equally spaced points along the X-axis starting
at 0.0 and ending at 1.0.</li>
+ <li>Trial:
+ <ul>
+ <li>Randomly Shuffles the input stream and presents it to the
sketch.</li>
+ <li>Executes <em>estRanks[] = getRanks(trueValues[])</em> from the
sketch where the array of <em>trueValues[]</em> are the 100 equally spaced
values along the x-axis that exactly correspond to the above Plot Points. The
<em>estRanks[]</em> is the array of the sketch’s estimates of the ranks of the
given <em>trueValues</em>.</li>
+ <li>Computes the absolute error: <em>estRanks[i] - trueRanks[i]</em> for
each Plot Point and submits this error to a corresponding array of standard
qantile sketches, with one quantile sketch assigned to each Plot Point.</li>
+ </ul>
+ </li>
+ <li>Trials:
+ <ul>
+ <li>2^12 random trials are executed. This produces a distribution of
error at each Plot Point held by the error quantile skeches.</li>
+ <li>Extract 7 quantiles from the error quantile sketches at each Plot
Point. These error quantiles correspond to the standard normal distribuion at
the median, +/- 1SD, +/- 2SD and +/- 3SD, where SD stands for Standard
Deviation from the mean.</li>
+ </ul>
+ </li>
+ <li>Plotting:
+ <ul>
+ <li>Each of the error quantiles are connected by lines to form contours
of the error distribution where the area between the +/- 1SD contours is the
size of the 68% confidence interval; between the +/- 2SD coutours is the 95.4%
confidence interval; and between the +/- 3SD contours is the 99.7% confidence
interval.</li>
+ <li>In addition to the error contours. 6 dashed contours (with colors
corresponding to the error contours) represent the a priori estimates of the
error at each of the +/- standard deviations computed from the sketch’s
<em>getRankLowerBound(double, int)</em> and <em>getRankUpperBound(double,
int)</em> methods.</li>
+ </ul>
+ </li>
+</ul>
+
+<h2 id="specific-configurations">Specific Configurations</h2>
+
+<h3 id="plot-1">Plot 1</h3>
+<ul>
+ <li>K=12: the sketch sizing & accuracy parameter</li>
+ <li>SL=2^20: StreamLength</li>
+ <li>HRA: High Rank Accuracy</li>
+ <li>Eq Spaced: Equally spaced Plot Points (PP)</li>
+ <li>PP=100: Number of plot points on the x-axis</li>
+ <li>LgT=12: Number of trials = 2^12</li>
+ <li>Crit=LT: Comparison criterion: LT = Less-Than</li>
+ <li>Shuffled: Random shuffle of the input stream for each trial</li>
+</ul>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK12SL20T12_LT_Sh.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<h3 id="plot-2">Plot 2</h3>
+<ul>
+ <li>K=12: the sketch sizing & accuracy parameter</li>
+ <li>SL=2^20: StreamLength</li>
+ <li>LRA: Low Rank Accuracy</li>
+ <li>Eq Spaced: Equally spaced Plot Points (PP)</li>
+ <li>PP=100: Number of plot points on the x-axis</li>
+ <li>LgT=12: Number of trials = 2^12</li>
+ <li>Crit=LE: Comparison criterion: LE = Less-Than or Equal</li>
+ <li>Shuffled: Random shuffle of the input stream for each trial</li>
+</ul>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqLraK12SL20T12_LE_Sh.png"
alt="/req/ReqErrEqLraK50SL20T12_LE_Sh.png" /></p>
+
+<h3 id="plot-3">Plot 3</h3>
+<ul>
+ <li>K=50: the sketch sizing & accuracy parameter</li>
+ <li>SL=2^20: StreamLength</li>
+ <li>HRA: High Rank Accuracy</li>
+ <li>Eq Spaced: Equally spaced Plot Points (PP)</li>
+ <li>PP=100: Number of plot points on the x-axis</li>
+ <li>LgT=12: Number of trials = 2^12</li>
+ <li>Crit=LT: Comparison criterion: LT = Less-Than</li>
+ <li>Shuffled: Random shuffle of the input stream for each trial</li>
+</ul>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqHraK50SL20T12_LT_Sh.png"
alt="/req/ReqErrEqHraK50SL20T12_LT_Sh.png" /></p>
+
+<h3 id="plot-4">Plot 4</h3>
+<ul>
+ <li>K=50: the sketch sizing & accuracy parameter</li>
+ <li>SL=2^20: StreamLength</li>
+ <li>LRA: Low Rank Accuracy</li>
+ <li>Eq Spaced: Equally spaced Plot Points (PP)</li>
+ <li>PP=100: Number of plot points on the x-axis</li>
+ <li>LgT=12: Number of trials = 2^12</li>
+ <li>Crit=LE: Comparison criterion: LE = Less-Than or Equal</li>
+ <li>Shuffled: Random shuffle of the input stream for each trial</li>
+</ul>
+
+<p><img class="doc-img-full"
src="/docs/img/req/ReqErrEqLraK50SL20T12_LE_Sh.png"
alt="/req/ReqErrEqLraK50SL20T12_LE_Sh.png" /></p>
+
+
+ </div> <!-- End content -->
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+
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+ <div class="container">
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+ <p>
+ <div>Copyright © 2020 <a href="https://www.apache.org";>Apache Software
Foundation</a>,
+ Licensed under the Apache License, Version 2.0. All Rights
Reserved.<br/>
+ Apache DataSketches, Apache, the Apache feather logo, and the Apache
DataSketches project logos are trademarks of The Apache Software
Foundation.<br/>
+ All other marks mentioned may be trademarks or registered trademarks
of their respective owners.<br/>
+ <br/>
+ <b>Disclaimer:</b> Apache DataSketches is an effort undergoing
incubation at The Apache Software Foundation (ASF), sponsored by the Apache
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