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AuthorDate: Wed Apr 15 19:27:40 2020 +0000
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---
output/docs/Architecture/SketchFeaturesMatrix.html | 63 ++++++++++++----------
output/docs/Community/Research.html | 2 +
output/docs/DistinctCountMeritComparisons.html | 2 +-
3 files changed, 37 insertions(+), 30 deletions(-)
diff --git a/output/docs/Architecture/SketchFeaturesMatrix.html
b/output/docs/Architecture/SketchFeaturesMatrix.html
index ad2a742..c51e12e 100644
--- a/output/docs/Architecture/SketchFeaturesMatrix.html
+++ b/output/docs/Architecture/SketchFeaturesMatrix.html
@@ -514,22 +514,22 @@
<tr
style="font-weight:bold"><td>Type</td><td>Sketch</td><td>Java</td><td>C++</td><td>Python</td><td>Union</td><td>Inter-section</td><td>Difference</td><td>Jaccard</td><td>Hive</td><td>Pig</td><td>Druid<sup>1</sup></td><td>Spark<sup>2</sup></td><td>PostgreSQL
(C++)</td><td>Con-current</td><td>Compact</td><td>Generic Types</td><td>Off
Java Heap</td><td>Error Bounds</td></tr>
-<tr style="font-weight:bold"><td colspan="18">Major Sketches</td></tr>
-<tr><td>Cardinality/FM85</td><td>CpcSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td>Y</td><td></td><td></td><td>Y</td></tr>
-<tr><td>Cardinality/FM85</td><td>HllSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td></tr>
+<tr style="font-weight:bold"><td colspan="19">Major Sketches</td></tr>
+<tr><td>Cardinality/CPC</td><td>CpcSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td>Y</td><td></td><td></td><td>Y</td></tr>
+<tr><td>Cardinality/HLL</td><td>HllSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td></tr>
<tr><td>Cardinality/Theta</td><td>Sketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y<sup>4</sup></td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td>Y</td><td>Y</td></tr>
<tr><td>Cardinality/Tuple</td><td>Sketch</td><td>Y</td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td>Y</td></tr>
<tr><td>Quantiles/Cormode</td><td>DoublesSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td><td>Y</td></tr>
<tr><td>Quantiles/Cormode</td><td>ItemsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
-<tr><td>Quantiles/KLL</td><td>FloatsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td>Y</td></tr>
-<tr><td>Quantiles/KLL</td><td>ItemsSketch</td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
-<tr><td>Frequencies</td><td>LongsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
+<tr><td>Quantiles/KLL</td><td>FloatsSketch</td><td>Y</td><td>Y</td><td>Y<sup>6</sup</td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td>Y</td></tr>
+<tr><td>Quantiles/KLL</td><td>ItemsSketch</td><td></td><td>Y</td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
+<tr><td>Frequencies</td><td>LongsSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
<tr><td>Frequencies</td><td>ItemsSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td>Y</td><td>Y</td><td></td><td></td><td>Y<sup>5</sup></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
-<tr><td>Sampling</td><td>ReservoirLongsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
-<tr><td>Sampling</td><td>ReserviorItemsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
-<tr><td>Sampling</td><td>VarOptItemsSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
+<tr><td>Sampling/Reservior</td><td>ReservoirLongsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
+<tr><td>Sampling/Reservoir</td><td>ReserviorItemsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
+<tr><td>Sampling/VarOpt</td><td>VarOptItemsSketch</td><td>Y</td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td>Y</td><td></td><td>Y</td></tr>
-<tr style="font-weight:bold"><td colspan="18">Specialty Sketches</td></tr>
+<tr style="font-weight:bold"><td colspan="19">Specialty Sketches</td></tr>
<tr><td>Cardinality/FM85</td><td>UniqueCountMap</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
<tr><td>Cardinality/Tuple</td><td>FdtSketch</td><td>Y</td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
@@ -538,31 +538,36 @@
<tr><td>Cardinality/Tuple</td><td>IntegerSketch</td><td>Y</td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
<tr><td>Cardinality/Tuple</td><td>ArrayOfStringsSketch</td><td>Y</td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
<tr><td>Cardinality/Tuple</td><td>EngagementTest<sup>3</sup></td><td>Y</td><td></td><td></td><td>Y</td><td>Y</td><td>Y</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>Y</td></tr>
-</table>
-</div>
+</table>
+</div>
+
+<sup>1</sup> Integrated into Druid.<br />
+<sup>2</sup> Spark Example Code on website. Theta Sketch is the only one we
have tried in Spark, it doesn't mean other sketches cannot be used.<br />
+<sup>3</sup> Tuple Sketch: Example Code in test/.../tuple/aninteger.<br />
+<sup>4</sup> Theta Sketch: C++/Python has no implementaion of the Jaccard,
yet.<br />
+<sup>5</sup> Frequent Items Sketch: PostgreSQL implemented for Strings
only.<br />
+<sup>6</sup> KLL Sketch: Python implemented for both just floats and ints.
+
+
+## Definitions
-<p><sup>1</sup> Integrated into Druid<br />
-<sup>2</sup> Example Code on website. Theta is the only sketch we have tried
in Spark, it doesn’t mean other sketches cannot be used in Spark.<br />
-<sup>3</sup> Example Code in test/…/tuple/aninteger.<br />
-<sup>4</sup> No Jaccard for Theta in C++/Python yet.<br />
-<sup>5</sup> PostgreSQL implemented Frequent Items Sketch for Strings only.</p>
+### Type
-<h2 id="definitions">Definitions</h2>
+See [Research/References](/docs/Community/Research.html) for references in
[...]
-<h3 id="type">Type</h3>
+* **Cardinality/CPC** Implementation and extension of [LAN17].
+* **Cardinality/HLL** Derivation and extension of [FFGM07]
+* **Cardinality/Theta** Derivation and extension of [DLRT16].
+* **Cardinality/Tuple** An Extension of the Theta family that adds attributes
to each hash-key.
+* **Quantiles/Cormode** Derivation and extension of [AC+13]
+* **Quantiles/KLL** Derivation and extension of [KLL16].
+* **Frequencies** Derivation and extension of [ABL+17].
+* **Sampling/Reservior** Derivation and extension of [K98], Vol 2, Section
3.4.2, Algorithm R.
+* **Sampling/VarOpt** Derivation and extension of [CDKLT09].
-<p>See <a href="/docs/Community/Research.html">Research</a> for references in
[…]</p>
-<ul>
- <li><strong>Cardinality/FM85</strong> Derivations of [FM85]. They include
the popular HyperLogLog (HLL) Sketch as well as the Compressed Probabilistic
Counting (CPC) Sketch, which has a completely different theoretical derivation
and is superior to the HLL sketch in terms of accuracy per byte of storage.</li>
- <li><strong>Cardinality/Theta</strong> Derivations of [BJKST02].</li>
- <li><strong>Cardinality/Tuple</strong> An Extension of the Theta family that
adds attributes to each hash-key.</li>
- <li><strong>Quantiles/Cormode</strong> Based on [AC+13]</li>
- <li><strong>Quantiles/KLL</strong> Based on [KLL16].</li>
- <li><strong>Frequencies</strong> Based on [ABL+17].</li>
- <li><strong>Sampling</strong> Two families, The simple reservoir sketch is
based on Knuth, algorithm R. The VarOpt sketch is based on [CDKLT09].</li>
-</ul>
+</sup></td></tr></table></div>
</div> <!-- End content -->
</div> <!-- End row -->
diff --git a/output/docs/Community/Research.html
b/output/docs/Community/Research.html
index 1f7a3f2..62b9658 100644
--- a/output/docs/Community/Research.html
+++ b/output/docs/Community/Research.html
@@ -609,6 +609,8 @@ and come with formal guarantees on the accuracy of the
answers returned.</p>
<p><strong>[GT02]</strong> Phillip B. Gibbons and Srikanta Tirthapura.
Distributed streams algorithms for sliding windows. In <em>ACM SPAA Proceedings
‘02</em>, pages 63–72, New York, NY, USA, 2002.</p>
+<p><strong>[K98]</strong> Donald E. Knuth. The Art of Computer Programming,
3rd Ed. 1998.</p>
+
<p><strong>[KLL16]</strong> Zohar S. Karnin, Kevin J. Lang, and Edo Liberty.
Optimal quantile approximation in streams. In <em>IEEE FOCS Proceedings
‘16</em>, pages 71–78, 2016.</p>
<p><strong>[Lan17]</strong> Kevin J Lang. Back to the future: an even more
nearly optimal cardinality estimation algorithm. In <em>arXiv preprint</em> <a
href="https://arxiv.org/abs/1708.06839">https://arxiv.org/abs/1708.06839</a>,
2017.</p>
diff --git a/output/docs/DistinctCountMeritComparisons.html
b/output/docs/DistinctCountMeritComparisons.html
index f66c389..d183584 100644
--- a/output/docs/DistinctCountMeritComparisons.html
+++ b/output/docs/DistinctCountMeritComparisons.html
@@ -606,7 +606,7 @@
<li>The relevant maximum values for each row was selected and effectively
set to 1.0.</li>
<li>The other relevant columns in that row were computed as a fractional
value between 0 and 1 with respect to the maximum value for that row.</li>
<li>The relevant columns for the HLL plot are columns 2, 3 and 4.</li>
- <li>The relevant columns for the HLL, CPC plot are clolumns 2, 3, 4 and
5.</li>
+ <li>The relevant columns for the HLL, CPC plot are columns 2, 3, 4 and
5.</li>
</ul>
<h2 id="reading-the-radar-charts">Reading the Radar Charts</h2>
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