blob: 4f0c8e728ba6a6bb6f97f874d3861f434faeac89 [file] [log] [blame]
<!DOCTYPE html>
<!-- Start _layouts/doc_page.html-->
<html lang="en">
<head>
<!-- Start _include/site_head.html -->
<meta charset="UTF-8" />
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="description" content="">
<meta name="author" content="datasketches">
<title>DataSketches | </title>
<link rel="shortcut icon" href="/img/favicon.png">
<!-- original source: https://maxcdn.bootstrapcdn.com/font-awesome/4.1.0/css/font-awesome.min.css -->
<link rel="stylesheet" href="/css/font-awesome.min.css">
<!-- original source: https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css -->
<link rel="stylesheet" href="/css/bootstrap.min.css">
<link rel="stylesheet" href="/css/fonts.css" type="text/css">
<link rel="stylesheet" href="/css/main.css">
<link rel="stylesheet" href="/css/header.css">
<link rel="stylesheet" href="/css/footer.css">
<link rel="stylesheet" href="/css/syntax.css">
<link rel="stylesheet" href="/css/docs.css">
<script type="text/x-mathjax-config">
MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]},showMathMenu:false,showMathMenuMSIE:false,showProcessingMessages:false});
</script>
<!-- original source: https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMX_HTML-full -->
<script type="text/javascript" src="/js/MathJax.js?config=TeX-AMS_HTML"></script>
<!-- original source: https://code.jquery.com/jquery.min.js -->
<script src="/js/jquery.min.js"></script>
<!-- original source: https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/js/bootstrap.min.js -->
<script src="/js/bootstrap.min.js"></script> <!-- 3.2.0-->
<!-- End _include/site_head.html -->
</head>
<body>
<!-- Start _include/nav_bar.html -->
<div class="navbar navbar-inverse navbar-static-top ds-nav">
<div class="container">
<div class="navbar-header">
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-collapse">
<span class="sr-only">Toggle navigation</span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
<span class="icon-bar"></span>
</button>
<a href="/" style="padding-top: 0px; padding-bottom: 0px;">
<span class="ds-small-h-logo"></span></a>
</div>
<div class="navbar-collapse collapse">
<ul class="nav navbar-nav navbar-right">
<li>
<a href="/docs/Background/TheChallenge.html">
<span class="fa fa-info-circle"></span> DOCUMENTATION</a>
</li>
<li>
<a href="/docs/Community/Downloads.html">
<span class="fa fa-download"></span> DOWNLOAD</a>
</li>
<!--
<li>
<a href="/docs/Architecture/Components.html">
<span class="fa fa-github"></span> GITHUB</a>
</li>
-->
<li>
<a href="/docs/Community/Research.html">
<span class="fa fa-paper-plane"></span> RESEARCH</a>
</li>
<li>
<a href="/docs/Community/index.html" style="padding-top: 0; padding-bottom: 0;">
<img class="ds-small-man" src="/img/datasketches-ManWhite.svg"/>COMMUNITY</a>
</li>
<li>
<ul class="nav navbar-nav navbar-right ds-nav">
<li class="dropdown ds-nav" >
<a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" aria-haspopup="true" aria-expanded="false" style="padding-top: 0; padding-bottom: 0;"><img class="apache-logo" src="/img/feather.svg"/>Apache <span class="caret"></span></a>
<ul class="dropdown-menu ds-nav">
<li><a href="https://www.apache.org/" target="_blank">Foundation</a></li>
<li><a href="https://www.apache.org/events/current-event" target="_blank">Events</a></li>
<li><a href="https://www.apache.org/licenses/" target="_blank">License</a></li>
<li><a href="https://privacy.apache.org/policies/privacy-policy-public.html" target="_blank">Privacy Policy</a></li>
<li><a href="https://www.apache.org/foundation/thanks.html" target="_blank">Thanks</a></li>
<li><a href="https://www.apache.org/security/" target="_blank">Security</a></li>
<li><a href="https://www.apache.org/foundation/sponsorship.html" target="_blank">Sponsorship</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
</div>
<!-- End _include/nav_bar.html -->
<!-- Start _include/javadocs.html -->
<div class="ds-header">
<div class="container">
<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>,
<a href="https://apache.github.io/datasketches-python/main/">Python</a>,
<a href="https://apache.github.io/datasketches-memory/master/">Memory</a>,
<a href="/api/pig/snapshot/apidocs/index.html">Pig</a>,
<a href="/api/hive/snapshot/apidocs/index.html">Hive</a>,
</h4>
</div>
</div>
<!-- End _include/javadocs.html -->
<div class="container">
<div class="row">
<!-- Start ToC Block -->
<div class="col-md-3">
<div class="searchbox" style="position:relative">
<gcse:searchbox-only></gcse:searchbox-only>
</div>
<!-- Start _includes/toc.html -->
<!-- Computer Generated File, Do Not Edit! -->
<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/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-component">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_memory_component">Memory Component</a>
</p>
<div class="collapse" id="collapse_memory_component">
<li><a href="/docs/Memory/MemoryComponent.html">•Memory Component</a></li>
<li><a href="/docs/Memory/MemoryPerformance.html">•Memory Component 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/ThetaSetOpsCornerCases.html">•Model & Test 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/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>
</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/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>
<div class="collapse" id="collapse_quantiles_studies">
<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>
</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/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>
<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>
</div>
<p id="research">
<a data-toggle="collapse" class="menu collapsed" href="#collapse_research">Research</a>
</p>
<div class="collapse" id="collapse_research">
<li><a href="/docs/Community/Research.html">•Research</a></li>
</div>
</div>
<!-- End _includes/toc.html -->
<!-- Start _includes/tocScript.html -->
<script>
(function () {
var findLineItem = function (path) {
return document.querySelector(`#toc [href="${path}"]`);
};
function findNavItem(path) {
return document.querySelector(`.nav [href="${path}"]`);
}
var highlighLineItem = function (element) {
element.classList.add('highlight');
};
var checkHasClass = function (element, className) {
return element.className.split(' ').find(function (item) { return item === className || '' })
}
var findAllCollapseParents = function (element) {
var collapseMenus = [];
var elementPointer = element;
while (elementPointer !== document.body) {
if (checkHasClass(elementPointer, 'collapse')) {
collapseMenus.push(elementPointer);
}
elementPointer = elementPointer.parentElement
}
return collapseMenus
};
var openMenuItem = function (element) {
// $(element).collapse('show') would start a transition, adding `in` class instead.
element.classList.add('in');
};
var openAllFromList = function (elementList) {
elementList.forEach(openMenuItem);
};
var highlightAndOpenMenu = function () {
// Highlight & expand nav item in the TOC
var currentLineItem = findLineItem(document.location.pathname);
highlighLineItem(currentLineItem);
openAllFromList(findAllCollapseParents(currentLineItem));
// Highlight nav item in top navigation
highlighLineItem(findNavItem(document.location.pathname));
};
$(highlightAndOpenMenu);
}());
</script>
<!-- End _includes/tocScript.html -->
</div>
<!-- End ToC Block -->
<div class="col-md-9 doc-content">
<!--
Licensed to the Apache Software Foundation (ASF) under one
or more contributor license agreements. See the NOTICE file
distributed with this work for additional information
regarding copyright ownership. The ASF licenses this file
to you under the Apache License, Version 2.0 (the
"License"); you may not use this file except in compliance
with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing,
software distributed under the License is distributed on an
"AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
KIND, either express or implied. See the License for the
specific language governing permissions and limitations
under the License.
-->
<h1 id="hll-sketch-vs-druid-hyperloglogcollector">HLL sketch vs Druid HyperLogLogCollector</h1>
<p>The goal of this article is to compare the HLL sketch implemented in this library to the <a href="https://github.com/apache/druid/tree/master/hll">Druid HyperLogLogCollector</a>.</p>
<h2 id="versions">Versions</h2>
<ul>
<li>HLL sketch form <a href="https://github.com/apache/datasketches-java">Java Version 0.11.1, April 20, 2018</a></li>
<li>Druid HyperLogLogCollector from <a href="https://github.com/apache/druid">Apache Druid Version 0.12.0, March 8, 2018</a></li>
</ul>
<h2 id="size">Size</h2>
<p>The starting point in this comparison was a choice of parameter <i>K=2048</i> for HLL sketch in such a way that it would approximately match the size of Druid HyperLogLogCollector, which has no parameters available to the user. It is quite difficult to measure the size of a Java object in memory, therefore the serialized size was used as the best available measure of size, which is also important for many practical applications in large systems.</p>
<p><img class="doc-img-full" src="/docs/img/hll/hll-sketch-vs-druid-size.png" alt="HLL2048 vs Druid HLLC serialized size plot" /></p>
<h2 id="single-sketch-accuracy">Single sketch accuracy</h2>
<p>The following plots are what we call pitch-fork plots. The X-axis is the number of distinct identifiers presented to the sketch. The Y-axis is the relative error plotted as +/- percent where values above zero represent an overestimate and values below zero represent an underestimate.</p>
<p><img class="doc-img-full" src="/docs/img/hll/hll-sketch-vs-druid-error-95pct.png" alt="HLL2048 vs Druid HLLC error 95% confidence interval plot" /></p>
<p><img class="doc-img-full" src="/docs/img/hll/hll-sketch-vs-druid-error-99pct.png" alt="HLL2048 vs Druid HLLC error 99% confidence interval plot" /></p>
<h2 id="merge-accuracy">Merge accuracy</h2>
<p>The HLL algorithm is fully mergeable. In simple terms this means that there should be no penalty for partitioning the input, processing these partitions separately, and finally merging the resulting sketches. The resulting estimate is required to be at least as accurate as if the whole input had been presented to a single sketch.</p>
<p>It was proved in <a href="http://algo.inria.fr/flajolet/Publications/FlFuGaMe07.pdf">Flajolet’s HLL paper</a> that for sufficiently large N and K, the standard error (i.e. the normalized RMS error) of HLL should be 1.0389 / sqrt(K), whether or not any merging has occurred. This guarantee works out to be about 2.3% when K = 2^11.</p>
<p>The following is an empirical demonstration that the library’s implementation of HLL exhibits the required behavior after merging, but Druid’s implementation of HLL does not. The latter’s measured standard error is about 7 times larger than HLL’s theoretical guarantee. This is mostly due to bias; on average, Druid is undercounting by about 16 percent on this example.</p>
<p>The test consisted of 100 trials of merging 8192 sketches into a single sketch. Each of the input sketches had been updated with 32768 unique values. The error is computed</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>Sketch Size: lgK = 11, k = 2048 True count: 2.68435456E8
Distinct keys per sketch = 32768
Number of sketches = 8192
Number of trials = 100 RSE Specification for this size sketch = 1.03896 / SQRT(2^11) = 0.023 = +/- 2.3% at 68% confidence.
The DataSketches library HLL implementation:
Mean estimate: 2.6826835125572532E8 (0.06 percent low, essentially no bias!)
Normalized RMS Error: 0.021226565654784535 (better than the RSE Specification)
Total Job Time : 0:07:33.241
The Druid HLL implementation:
Mean estimate: 2.2560974267493743E8 (16 percent low)
Normalized RMS Error: 0.16058739888244847 (7 times the RSE Specification)
Total Job Time : 0:36:43.451
</code></pre></div></div>
<p>Also, Druid’s implementation was much slower.</p>
<p>The above comparisons can be visualized in the following charts:</p>
<p><img class="doc-img-half" src="/docs/img/hll/DruidRSEComparison.png" alt="HLL2048 vs Druid HLLC Merge error" />
<img class="doc-img-half" src="/docs/img/hll/DruidBuildMergeTimeComparison.png" alt="HLL2048 vs Druid Merge Time" />
<img class="doc-img-half" src="/docs/img/hll/DruidHllBiasComparison.png" alt="HLL2048 vs Druid Bias" /></p>
<p>Technical Note: the library’s HLL sketches are more complicated than the standard HLL algorithm. In certain special cases where better-than-HLL accuracy is possible, the library employs other estimators, and even other stochastic processes and data structures. When those special cases no longer apply, the library falls back to the standard HLL estimator algorithm.
One of these special cases is for a simple streaming sketch that is not involved in merge operations we can take advantage of a more advanced estimator algorithm with improved error properties.
When comparing the error of a merged sketch to the error of a non-merged sketch, the library’s HLL sketches will have a slightly larger error after merging. This is the direct result of this fall-back mechanism.
This slightly larger error is still within the RSE Specification of error defined as 1.03896 / SQRT(k).</p>
<h2 id="source-code">Source code</h2>
<p>The code to reproduce these measurements is available in the <a href="https://github.com/apache/datasketches-characterization">Datasketches/characterization repository</a></p>
<h2 id="datasketches-hll-sketch-druid-module">DataSketches HLL Sketch Druid module</h2>
<p>The DataSketches Hll sketch module for Druid is available as a part of <a href="https://datasketches.apache.org/docs/SystemIntegrations/ApacheDruidIntegration.html">Druid/Extensions-core</a></p>
</div> <!-- End content -->
</div> <!-- End row -->
</div> <!-- End Container -->
<!-- Start _include/page_footer.html -->
<footer class="ds-footer">
<div class="container">
<div class="text-center">
<p>
<div>Copyright © 2024 <a href="https://www.apache.org">Apache Software Foundation</a>,
Licensed under the Apache License, Version 2.0. All Rights Reserved.
| <a href="https://privacy.apache.org/policies/privacy-policy-public.html">Privacy Policy</a><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.
</div>
</p>
</div>
</div>
</footer>
<!-- End _include/page_footer.html -->
</body>
</html>
<!-- End _layouts/doc_page.html-->