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commit 95f671761771b54e17695f6a2d36f1f83375ff9a
Author: buildbot <us...@infra.apache.org>
AuthorDate: Mon Oct 19 15:58:28 2020 +0000
Automatic Site Publish by Buildbot
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@@ -0,0 +1,552 @@
+<!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">
+
+<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/font-awesome/4.1.0/css/font-awesome.min.css">
+<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/css/bootstrap.min.css">
+
+<link href='https://fonts.googleapis.com/css?family=Open+Sans+Condensed:300,700,300italic|Open+Sans:300italic,400italic,600italic,400,300,600'
+ rel='stylesheet' type='text/css'>
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+<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">
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+</script>
+<script src="https://code.jquery.com/jquery.min.js"></script>
+<script src="https://maxcdn.bootstrapcdn.com/bootstrap/3.2.0/js/bootstrap.min.js"></script>
+<!-- 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>
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+</div>
+<!-- End _include/nav_bar.html -->
+
+<!-- Start _include/javadocs.html -->
+<div class="ds-header">
+ <div class="container">
+ <h4>API Snapshots:
+ <a href="/api/java/snapshot/apidocs/index.html">Java Core</a>,
+ <a href="/api/memory/snapshot/apidocs/index.html">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/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>
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+ </div>
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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>
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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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+ <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 Incubator. Incubation is required of all newly accepted projects until a further review indicates that the infrastructure, communications, and decision making process have stabilized in a manner consistent with other successful ASF projects. While incubation status is not necessarily a reflection of the completeness or stability of the code, [...]
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+<div id="toc" class="nav toc hidden-print">
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+ <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>
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+ <a data-toggle="collapse" class="menu collapsed" href="#collapse_distinct_counting">Distinct Counting</a>
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+ <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>
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+ <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>
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+ <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>
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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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+ <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>
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+ <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>
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+
+ <p id="most-frequent-examples">
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+ <li><a href="/docs/Frequency/FrequentItemsPigUDFs.html">•Frequent Items Pig 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>
+ </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>
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+ <li><a href="/docs/Quantiles/QuantilesJavaExample.html">•Quantiles Sketch Java Example</a></li>
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+ <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/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>
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+ <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>
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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/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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+ <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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+<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>
+
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+ <div class="text-center">
+ <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 Incubator. Incubation is required of all newly accepted projects until a further review indicates that the infrastructure, communications, and decision making process have stabilized in a manner consistent with other successful ASF projects. While incubation status is not necessarily a reflection of the completeness or stability of the code, [...]
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