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<h4>API Snapshots:
<a href="https://apache.github.io/datasketches-java/4.2.0/">Java Core</a>,
<a href="https://apache.github.io/datasketches-cpp/5.0.0/">C++ Core</a>,
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<p id="background">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_background">Background</a>
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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>
<li><a href="https://github.com/apache/datasketches-website/tree/master/docs/pdf/DataSketches_deck.pdf">•Overview Slide Deck</a></li>
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<p id="architecture-and-design">
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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>
<p id="memory-component">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_memory_component">Memory Component</a>
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<li><a href="/docs/Memory/MemoryComponent.html">•Memory Component</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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<p id="sketch-families">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_sketch_families">Sketch Families</a>
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<p id="distinct-counting">
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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">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_cpc_sketches">CPC Sketches</a>
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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>
<p id="cpc-examples">
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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">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_hyperloglog_sketches">HyperLogLog Sketches</a>
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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>
<p id="hll-examples">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_hll_examples">HLL Examples</a>
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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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<p id="theta-sketches">
<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">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_examples">Theta Examples</a>
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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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<p id="kmv-tutorial">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_kmv_tutorial">KMV Tutorial</a>
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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">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_set_operations_and_p-sampling">Set Operations and P-sampling</a>
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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">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_size">Size</a>
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<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>
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<p id="theta-sketch-theory">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_theta_sketch_theory">Theta Sketch Theory</a>
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<div class="collapse" id="collapse_theta_sketch_theory">
<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>
<p id="tuple-examples">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_tuple_examples">Tuple Examples</a>
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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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</div>
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<p id="most-frequent">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_most_frequent">Most Frequent</a>
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<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>
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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>
<p id="most-frequent-examples">
<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>
</div>
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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>
</div>
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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>
</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/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>
</div>
<p id="quantiles-studies">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_quantiles_studies">Quantiles Studies</a>
</p>
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<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>
</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>
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<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>
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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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<p id="research">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_research">Research</a>
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<li><a href="/docs/Community/Research.html">•Research</a></li>
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<h2 id="key-features">Key Features</h2>
<h3 id="sketch-features-matrix"><a href="/docs/Architecture/SketchFeaturesMatrix.html">Sketch Features Matrix</a></h3>
<h3 id="common-sketch-properties">Common Sketch Properties</h3>
<ul>
<li>Please refer to the <a href="/docs/Architecture/SketchCriteria.html">Sketch Criteria</a> for the criteria for sketches to be included in the library.</li>
<li>Query results are <b>approximate</b> but within well defined error bounds that are user
configurable by trading off sketch size with accuracy.</li>
<li>Designed for <a href="/docs/Architecture/LargeScale.html">Large-scale</a> computing environments
that must handle <b>Big Data</b>, e.g.:
<ul>
<li><a href="https://hadoop.apache.org/">Hadoop</a></li>
<li><a href="https://pig.apache.org">Pig</a></li>
<li><a href="https://hive.apache.org">Hive</a></li>
<li><a href="https://druid.apache.org">Druid</a></li>
<li><a href="https://spark.apache.org">Spark</a></li>
</ul>
</li>
<li>
<table>
<tbody>
<tr>
<td><b>Maven deployable</b> and registered with the [Central Repository](https://search.maven.org/#search</td>
<td>ga</td>
<td>1</td>
<td>DataSketches).</td>
</tr>
</tbody>
</table>
</li>
<li>Extensive documentation with the systems developer in mind.</li>
<li>Designed for production environments:
<ul>
<li>Available in multiple languages: Java, C++, <a href="https://github.com/apache/datasketches-cpp/tree/master/python">Python</a></li>
<li>Binary compatible across systems and languages</li>
</ul>
</li>
</ul>
<h3 id="built-in-general-purpose-functions">Built-In, General Purpose Functions</h3>
<ul>
<li>General purpose <a href="/docs/Memory/MemoryComponent.html">Memory Component</a> for managing data off the Java Heap.
This enables systems designers the ability to manage their own large data heaps with
dedicated processor threads that would otherwise put undue pressure on the Java heap and
its garbage collection.</li>
<li>General purpose implementaion of Austin Appleby’s 128-bit MurmurHash3 algorithm,
with a number of useful extensions.</li>
</ul>
<h3 id="robust-high-quality-implementations">Robust, High Quality Implementations.</h3>
<ul>
<li>Unit Tests:
<ul>
<li>Extensive test code leveraging <a href="https://testng.org">TestNG</a>.</li>
<li>High Test Code coverage (&gt; 90%) as measured by [JaCoCo]https://www.eclemma.org/jacoco) and published by
<a href="https://coveralls.io">Coveralls</a>.</li>
</ul>
</li>
<li>Reproducible Characterization Studies
<ul>
<li>All our published speed and accuracy performance results can be reproduced using the code included in the
<a href="https://github.com/apache/datasketches-characterization">Characterization</a> repository.</li>
</ul>
</li>
<li>Comprehensive Javadocs that satisfy
<a href="https://docs.oracle.com/javase/8/docs/technotes/guides/javadoc/index.html">JDK8 Javadoc</a> standards.</li>
</ul>
<h3 id="opportunities-to-extend">Opportunities to Extend</h3>
<ul>
<li>There is ample opportunity for interested parties to contribute additional algorithms in this exciting area.</li>
</ul>
<h2 id="key-algorithms">Key Algorithms</h2>
<h3 id="count-distinct--count-unique">Count Distinct / Count Unique</h3>
<h4 id="solves-computational-challenges-associated-with-unique-identifiers">Solves Computational Challenges Associated with Unique Identifiers</h4>
<ul>
<li><b>Estimating cardinality</b> of a stream with many duplicates</li>
<li>Performing <a href="/docs/Theta/ThetaSketchSetOps.html">Set Operations</a> (e.g., Union, Intersection,
and Difference) on sets of unique identifiers</li>
<li>Estimates of the <b>error bounds</b> of the result can be obtained directly from the result sketch</li>
</ul>
<h4 id="four-families-of-count-unique-algorithms">Four families of Count Unique algorithms:</h4>
<ul>
<li><a href="/docs/HLL/HLL.html">The HLL Sketch</a>. The famous HyperLogLog algorithm when stored sketch size is of utmost concern.</li>
<li><a href="/docs/CPC/CPC.html">The CPC Sketch</a>. The Compressed Probabilistic Counting algorithm when maximizing accuracy per stored sketch size is of utmost concern.</li>
<li><a href="/docs/Theta/ThetaSketchFramework.html">The Theta Sketch Framework</a>. Theta sketches enable real-time set-expression computations and can operate on or off the java heap.</li>
<li><a href="/docs/Tuple/TupleOverview.html">The Tuple Sketch</a>. Tuple sketches are associative sketches that are useful for performing approximate join operations and extracting other kinds of statistical behavior associated with unique identifiers.</li>
</ul>
<h3 id="quantiles">Quantiles</h3>
<ul>
<li><a href="/docs/Quantiles/QuantilesSketchOverview.html">Quantiles Sketch Overview</a>. Get normal or inverse PDFs or CDFs of the distributions of any numeric value from your raw data in a single pass with well defined error bounds on the results.</li>
</ul>
<h3 id="frequent-items">Frequent Items</h3>
<ul>
<li><a href="/docs/Frequency/FrequencySketchesOverview.html">Frequent Items Sketches</a> Get the most frequent items from a stream of items.</li>
</ul>
<h3 id="sampling">Sampling</h3>
<ul>
<li><a href="/docs/Sampling/ReservoirSampling.html">Reservoir Sampling</a> Knuth’s well known Reservoir sampling “Algorithm R”, but extended to enable merging across different sized reservoirs.</li>
<li><a href="/docs/Sampling/VarOptSampling.html">Weighted Sampling</a> Edith Cohen’s famous sampling algorithm that enables computing subset sums of weighted samples with optimum variance.</li>
</ul>
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