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<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>
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<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>
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<li><a href="/docs/Memory/MemoryComponent.html">•Memory Componet</a></li>
<li><a href="/docs/Memory/MemoryPerformance.html">•Memory Component Performance</a></li>
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<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>
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<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">
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<li><a href="/docs/CPC/CPC.html">•CPC Sketch</a></li>
<li><a href="/docs/CPC/CpcPerformance.html">•CPC Sketch Performance</a></li>
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<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>
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<p id="hyperloglog-sketches">
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<li><a href="/docs/HLL/HLL.html">•HLL Sketch</a></li>
<li><a href="/docs/HLL/HllMap.html">•HLL Map Sketch</a></li>
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<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>
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<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>
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<a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_sketches">Theta Sketches</a>
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<li><a href="/docs/Theta/ThetaSketchFramework.html">•Theta Sketch Framework</a></li>
<p id="theta-examples">
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<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>
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<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>
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<p id="set-operations-and-p-sampling">
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<li><a href="/docs/Theta/ThetaSketchSetOps.html">•Set Operations</a></li>
<li><a href="/docs/Theta/ThetaSetOpsCornerCases.html">•Model & Test Set Operations</a></li>
<li><a href="/docs/Theta/ThetaPSampling.html"><i>p</i>-Sampling</a></li>
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<p id="accuracy">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_accuracy">Accuracy</a>
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<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>
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<p id="size">
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<li><a href="/docs/Theta/ThetaSize.html">•Theta Sketch Size</a></li>
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<p id="speed">
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<li><a href="/docs/Theta/ThetaUpdateSpeed.html">•Update Speed</a></li>
<li><a href="/docs/Theta/ThetaMergeSpeed.html">•Merge Speed</a></li>
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<a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_sketch_theory">Theta Sketch Theory</a>
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<li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/ThetaSketchFramework.pdf">•Theta Sketch Framework (PDF)</a></li>
<li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/ThetaSketchEquations.pdf">•Theta Sketch Equations (PDF)</a></li>
<li><a href="https://github.com/apache/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>
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<p id="tuple-sketches">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_tuple_sketches">Tuple Sketches</a>
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<li><a href="/docs/Tuple/TupleOverview.html">•Tuple Overview</a></li>
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<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>
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<p id="most-frequent">
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<li><a href="/docs/Frequency/FrequencySketchesOverview.html">•Frequency Sketches Overview</a></li>
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<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>
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<a data-toggle="collapse" class="menu collapsed" href="#collapse_most_frequent_examples">Most Frequent Examples</a>
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<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>
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<p id="frequent-distinct-sketches">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_frequent_distinct_sketches">Frequent Distinct Sketches</a>
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<li><a href="/docs/Frequency/FrequentDistinctTuplesSketch.html">•Frequent Distinct Tuples Sketch</a></li>
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<p id="quantiles-and-histograms">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_and_histograms">Quantiles And Histograms</a>
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<li><a href="/docs/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and Ranks Tutorial</a></li>
<li><a href="/docs/Quantiles/QuantilesOverview.html">•Quantiles Overview</a></li>
<li><a href="/docs/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
<li><a href="/docs/KLL/KLLAccuracyAndSize.html">•KLL Sketch Accuracy and Size</a></li>
<li><a href="/docs/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
<li><a href="/docs/Quantiles/OrigQuantilesSketch.html">•Original QuantilesSketch</a></li>
<p id="quantiles-examples">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_examples">Quantiles Examples</a>
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<li><a href="/docs/Quantiles/QuantilesJavaExample.html">•Quantiles Sketch Java Example</a></li>
<li><a href="/docs/KLL/KLLCppExample.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>
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<p id="quantiles-studies">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_studies">Quantiles Studies</a>
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<li><a href="/docs/QuantilesStudies/KllSketchVsTDigest.html">•KLL sketch vs t-digest</a></li>
<li><a href="/docs/QuantilesStudies/DruidApproxHistogramStudy.html">•Druid Approximate Histogram</a></li>
<li><a href="/docs/QuantilesStudies/MomentsSketchStudy.html">•Moments Sketch Study</a></li>
<li><a href="/docs/QuantilesStudies/QuantilesStreamAStudy.html">•Quantiles StreamA Study</a></li>
<li><a href="/docs/QuantilesStudies/ExactQuantiles.html">•Exact Quantiles for Studies</a></li>
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<p id="quantiles-sketch-theory">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_sketch_theory">Quantiles Sketch Theory</a>
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<li><a href="https://github.com/apache/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>
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<p id="sampling">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_sampling">Sampling</a>
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<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>
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<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>
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<p id="system-integrations">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_system_integrations">System Integrations</a>
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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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<a data-toggle="collapse" class="menu collapsed" href="#collapse_community">Community</a>
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<li><a href="/docs/Community/index.html">•Community</a></li>
<li><a href="/docs/Community/Downloads.html">•Downloads</a></li>
<li><a href="/docs/Community/NewCommitterProcess.html">•Committer Process</a></li>
<li><a href="/docs/Community/ReleaseProcessForCppComponents.html">•Release Process For CPP Components</a></li>
<li><a href="/docs/Community/ReleaseProcessForJavaComponents.html">•Release Process For Java Components</a></li>
<li><a href="/docs/Community/Transitioning.html">•Transitioning from prior GitHub Site</a></li>
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<h1 id="introduction-to-the-3-quantiles-sketches">Introduction to the 3 Quantiles Sketches</h1>
<h2 id="quantile-type-sketches-in-the-library">Quantile-type sketches in the library</h2>
<p>This is an overview of the three types of quantiles sketches in the library. Each of these quantile types may have one or more specific implementtaions.</p>
<p>The mathematical error bounds of all the quantile sketches is specified with respect to rank and not with respect to quantiles. In other words, the difference between the rank upper bound and the rank lower bound is the confidence interval and can be expressed as a percent of the overall rank distribution (which is 1.0) and is the mathematically derived error for a specific configuration of the sketch.</p>
<p>Although the quantile upper bound and quantile lower bounds can be approximately computed from the rank upper bound and rank lower bound, and the difference between the quantile bounds is also an approximate confidence interval, the size of the quantile confidence interval may not be meaningful and is not constrained by the defined error of the sketch.</p>
<p>These sketches have many parallel methods. Please refer to the individual Javadocs for more information.</p>
<h3 id="the-req-sketch">The REQ Sketch</h3>
<ul>
<li>Java
<ul>
<li>Release 2.0.0, 12 Feb 2021</li>
<li>Repo: <a href="https://github.com/apache/datasketches-java">https://github.com/apache/datasketches-java</a></li>
<li>Package: org.apache.datasketches.req</li>
</ul>
</li>
<li>C++, Python
<ul>
<li>Release 2.2.0, Soon</li>
<li>Repo: <a href="https://github.com/apache/datasketches-cpp">https://github.com/apache/datasketches-cpp</a></li>
<li>Directory: req</li>
</ul>
</li>
<li>Key Features (both Java &amp; C++)
<ul>
<li>Accuracy %: a function of <em>K</em> and <strong>relative</strong> with respect to rank. The user can select either High Rank Accuracy (HRA) or Low Rank Accuracy (LRA). This enables extremely high accuracy for the ends of the rank domain. E.g., 99.999%ile quantiles.</li>
<li>User selectable comparison QuantileSearchCriteria:
<ul>
<li>Exclusive, which is compatible with the KLL and older Quantiles Sketch</li>
<li>Inclusive, a common definition in some of the theoretical literature.</li>
</ul>
</li>
<li>Java: Dedicated <em>float</em> implementation.</li>
<li>C++: Template implementation for arbitrary comparible types.</li>
<li>Python: Dedicated <em>float</em> and <em>integer</em> implementations.</li>
</ul>
</li>
</ul>
<h3 id="the-kll-sketch">The KLL Sketch</h3>
<ul>
<li>Java
<ul>
<li>Release 0.11.0, 15 Mar 2018</li>
<li>Repo: <a href="https://github.com/apache/datasketches-java">https://github.com/apache/datasketches-java</a>:</li>
<li>Package: org.apache.datasketches.kll</li>
</ul>
</li>
<li>C++, Python
<ul>
<li>Release 1.0.0, 17 Sep 2019</li>
<li>Repo: <a href="https://github.com/apache/datasketches-cpp">https://github.com/apache/datasketches-cpp</a></li>
<li>Directory: kll</li>
</ul>
</li>
<li>Key Features (both Java &amp; C++)
<ul>
<li>User selectable comparison QuantileSearchCriteria:
<ul>
<li>Exclusive, which is compatible with the KLL and older Quantiles Sketch</li>
<li>Inclusive, a common definition in some of the theoretical literature.</li>
</ul>
</li>
<li>Accuracy %: a function of <em>K</em> and independent of rank.</li>
<li>Near optimal accuracy per sketch size compared to other constant accuracy quantiles sketches.</li>
<li>Java: Dedicated <em>float</em> and <em>double</em> implementations.</li>
<li>C++: Template implementation for arbitrary comparible types.</li>
<li>Python: Dedicated <em>float</em> and <em>integer</em> implementations</li>
</ul>
</li>
</ul>
<h3 id="the-quantiles-sketch">The Quantiles Sketch</h3>
<ul>
<li>Java
<ul>
<li>Release 0.3.0, 25 Jan 2016</li>
<li>Repo: <a href="https://github.com/apache/datasketches-java">https://github.com/apache/datasketches-java</a></li>
<li>Package: org.apache.datasketches.quantiles</li>
</ul>
</li>
<li>C++, Python
<ul>
<li>Release 1.0.0, 17 Sep 2019</li>
<li>Repo: <a href="https://github.com/apache/datasketches-cpp">https://github.com/apache/datasketches-cpp</a></li>
<li>Directory:</li>
</ul>
</li>
<li>Key Features (both Java &amp; C++)
<ul>
<li>User selectable comparison QuantileSearchCriteria:
<ul>
<li>Exclusive, which is compatible with the KLL and older Quantiles Sketch</li>
<li>Inclusive, a common definition in some of the theoretical literature.</li>
</ul>
</li>
<li>Accuracy %: a function of <em>K</em> and independent of rank.</li>
<li>Dedicated <em>double</em> implentation.</li>
<li>java generic implementation for arbitrary comparible types.</li>
<li>The dedicated <em>double</em> implementation can be configured for off-heap operation.</li>
</ul>
</li>
</ul>
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