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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="{{site.docs_dir}}/Background/TheChallenge.html">•The Challenge</a></li>
    <li><a href="{{site.docs_dir}}/Background/SketchOrigins.html">•Sketch Origins</a></li>
    <li><a href="{{site.docs_dir}}/Background/SketchElements.html">•Sketch Elements</a></li>
    <li><a href="{{site.docs_dir}}/Background/Presentations.html">•Presentations</a></li>
    <li><a href="{{site.docs_pdf_dir}}/DataSketches_deck.pdf">•Overview Slide Deck</a></li>
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  <p id="architecture-and-design">
    <a data-toggle="collapse" class="menu collapsed" href="#collapse_architecture_and_design">Architecture And Design</a>
  </p>
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    <li><a href="{{site.docs_dir}}/Architecture/MajorSketchFamilies.html">•The Major Sketch Families</a></li>
    <li><a href="{{site.docs_dir}}/Architecture/LargeScale.html">•Large Scale Computing</a></li>
    <li><a href="{{site.docs_dir}}/Architecture/KeyFeatures.html">•Key Features</a></li>
    <li><a href="{{site.docs_dir}}/Architecture/SketchFeaturesMatrix.html">•Sketch Features Matrix</a></li>
    <li><a href="{{site.docs_dir}}/Architecture/Components.html">•Components</a></li>
    <li><a href="{{site.docs_dir}}/Architecture/SketchesByComponent.html">•Sketches by Component</a></li>
    <li><a href="{{site.docs_dir}}/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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    <div class="collapse" id="collapse_memory_component">
      <li><a href="{{site.docs_dir}}/Memory/MemoryComponent.html">•Memory Componet</a></li>
      <li><a href="{{site.docs_dir}}/Memory/MemoryPerformance.html">•Memory Component Performance</a></li>
    </div>
    <li><a href="{{site.docs_dir}}/Architecture/OrderSensitivity.html">•Notes on Order Sensitivity</a></li>
    <li><a href="{{site.docs_dir}}/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">
      <a data-toggle="collapse" class="menu collapsed" href="#collapse_distinct_counting">Distinct Counting</a>
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      <li><a href="{{site.docs_dir}}/DistinctCountFeaturesMatrix.html">•Features Matrix</a></li>
      <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/CPC/CPC.html">•CPC Sketch</a></li>
        <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/CPC/CpcJavaExample.html">•CPC Sketch Java Example</a></li>
          <li><a href="{{site.docs_dir}}/CPC/CpcCppExample.html">•CPC Sketch C++ Example</a></li>
          <li><a href="{{site.docs_dir}}/CPC/CpcPigExample.html">•CPC Sketch Pig UDFs</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/HLL/HLL.html">•HLL Sketch</a></li>
        <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/HLL/HllJavaExample.html">•HLL Sketch Java Example</a></li>
          <li><a href="{{site.docs_dir}}/HLL/HllCppExample.html">•HLL Sketch C++ Example</a></li>
          <li><a href="{{site.docs_dir}}/HLL/HllPigUDFs.html">•HLL Sketch Pig UDFs</a></li>
          <li><a href="{{site.docs_dir}}/HLL/HllHiveUDFs.html">•HLL Sketch Hive UDFs</a></li>
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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="{{site.docs_dir}}/HLL/HllPerformance.html">•HLL Sketch Performance</a></li>
          <li><a href="{{site.docs_dir}}/HLL/Hll_vs_CS_Hllpp.html">•HLL vs Clearspring HLL++</a></li>
          <li><a href="{{site.docs_dir}}/HLL/HllSketchVsDruidHyperLogLogCollector.html">•HLL Sketch vs Druid HyperLogLogCollector</a></li>
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      </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="{{site.docs_dir}}/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="{{site.docs_dir}}/Theta/ConcurrentThetaSketch.html">•Concurrent Theta Sketch</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaJavaExample.html">•Theta Sketch Java Example</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaSparkExample.html">•Theta Sketch Spark Example</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaPigUDFs.html">•Theta Sketch Pig UDFs</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/Theta/InverseEstimate.html">•The Inverse Estimate</a></li>
          <li><a href="{{site.docs_dir}}/Theta/KMVempty.html">•Empty Sketch</a></li>
          <li><a href="{{site.docs_dir}}/Theta/KMVfirstEst.html">•First Estimator</a></li>
          <li><a href="{{site.docs_dir}}/Theta/KMVbetterEst.html">•Better Estimator</a></li>
          <li><a href="{{site.docs_dir}}/Theta/KMVrejection.html">•Rejection Rules</a></li>
          <li><a href="{{site.docs_dir}}/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>
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        <div class="collapse" id="collapse_set_operations_and_p-sampling">
          <li><a href="{{site.docs_dir}}/Theta/ThetaSketchSetOps.html">•Set Operations</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaSetOpsCornerCases.html">•Model & Test Set Operations</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/Theta/ThetaAccuracy.html">•Basic Accuracy</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaAccuracyPlots.html">•Accuracy Plots</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaErrorTable.html">•Relative Error Table</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaSketchSetOpsAccuracy.html">•SetOp Accuracy</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/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="{{site.docs_dir}}/Theta/ThetaUpdateSpeed.html">•Update Speed</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_pdf_dir}}/ThetaSketchFramework.pdf">•Theta Sketch Framework (PDF)</a></li>
          <li><a href="{{site.docs_pdf_dir}}/ThetaSketchEquations.pdf">•Theta Sketch Equations (PDF)</a></li>
          <li><a href="{{site.docs_pdf_dir}}/DataSketches.pdf">•DataSketches (PDF)</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaConfidenceIntervals.html">•Confidence Intervals Notes</a></li>
          <li><a href="{{site.docs_dir}}/Theta/ThetaMergingAlgorithm.html">•Merging Algorithm Notes</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/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="{{site.docs_dir}}/Tuple/TupleJavaExample.html">•Tuple Java Example</a></li>
          <li><a href="{{site.docs_dir}}/Tuple/TupleEngagementExample.html">•Tuple Engagement Example</a></li>
          <li><a href="{{site.docs_dir}}/Tuple/TuplePigUDFs.html">•Tuple Pig UDFs</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/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="{{site.docs_dir}}/Frequency/FrequentItemsOverview.html">•Frequent Items Overview</a></li>
        <li><a href="{{site.docs_dir}}/Frequency/FrequentItemsErrorTable.html">•Frequent Items Error Table</a></li>
        <li><a href="{{site.docs_dir}}/Frequency/FrequentItemsReferences.html">•Frequent Items References</a></li>
        <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/Frequency/FrequentItemsJavaExample.html">•Frequent Items Java Example</a></li>
          <li><a href="{{site.docs_dir}}/Frequency/FrequentItemsCppExample.html">•Frequent Items C++ Example</a></li>
          <li><a href="{{site.docs_dir}}/Frequency/FrequentItemsPigUDFs.html">•Frequent Items Pig UDFs</a></li>
          <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/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="{{site.docs_dir}}/Quantiles/SketchingQuantilesAndRanksTutorial.html">•Quantiles and Ranks Tutorial</a></li>
      <li><a href="{{site.docs_dir}}/Quantiles/QuantilesOverview.html">•Quantiles Overview</a></li>
      <li><a href="{{site.docs_dir}}/KLL/KLLSketch.html">•KLL Floats sketch</a></li>
      <li><a href="{{site.docs_dir}}/REQ/ReqSketch.html">•REQ Floats sketch</a></li>
      <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/Quantiles/QuantilesJavaExample.html">•Quantiles Sketch Java Example</a></li>
        <li><a href="{{site.docs_dir}}/KLL/KLLCppExample.html">•KLL Quantiles Sketch C++ Example</a></li>
        <li><a href="{{site.docs_dir}}/Quantiles/QuantilesPigUDFs.html">•Quantiles Sketch Pig UDFs</a></li>
        <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/QuantilesStudies/KllSketchVsTDigest.html">•KLL sketch vs t-digest</a></li>
        <li><a href="{{site.docs_dir}}/QuantilesStudies/DruidApproxHistogramStudy.html">•Druid Approximate Histogram</a></li>
        <li><a href="{{site.docs_dir}}/QuantilesStudies/MomentsSketchStudy.html">•Moments Sketch Study</a></li>
        <li><a href="{{site.docs_dir}}/QuantilesStudies/QuantilesStreamAStudy.html">•Quantiles StreamA Study</a></li>
        <li><a href="{{site.docs_dir}}/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="{{site.docs_pdf_dir}}/Quantiles_KLL.pdf">•Optimal Quantile Approximation in Streams</a></li>
        <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/Sampling/ReservoirSampling.html">•Reservoir Sampling</a></li>
      <li><a href="{{site.docs_dir}}/Sampling/ReservoirSamplingPerformance.html">•Reservoir Sampling Performance</a></li>
      <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/Sampling/ReservoirSamplingJava.html">•Reservoir Sampling Java Example</a></li>
        <li><a href="{{site.docs_dir}}/Sampling/ReservoirSamplingPigUDFs.html">•Reservoir Sampling Pig UDFs</a></li>
        <li><a href="{{site.docs_dir}}/Sampling/VarOptSamplingJava.html">•VarOpt Sampling Java Example</a></li>
        <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/SystemIntegrations/ApacheDruidIntegration.html">•Using Sketches in ApacheDruid</a></li>
    <li><a href="{{site.docs_dir}}/SystemIntegrations/ApacheHiveIntegration.html">•Using Sketches in Apache Hive</a></li>
    <li><a href="{{site.docs_dir}}/SystemIntegrations/ApachePigIntegration.html">•Using Sketches in Apache Pig</a></li>
    <li><a href="{{site.docs_dir}}/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="{{site.docs_dir}}/Community/index.html">•Community</a></li>
    <li><a href="{{site.docs_dir}}/Community/Downloads.html">•Downloads</a></li>
    <li><a href="{{site.docs_dir}}/Community/NewCommitterProcess.html">•Committer Process</a></li>
    <li><a href="{{site.docs_dir}}/Community/ReleaseProcessForCppComponents.html">•Release Process For CPP Components</a></li>
    <li><a href="{{site.docs_dir}}/Community/ReleaseProcessForJavaComponents.html">•Release Process For Java Components</a></li>
    <li><a href="{{site.docs_dir}}/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>
  </p>
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    <li><a href="{{site.docs_dir}}/Community/Research.html">•Research</a></li>
  </div>
</div>
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