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      <p class="lead" style="font-size: 20px; line-height: 1.0; margin-bottom: 15px; color: #FFFFFF">A software library of 
        <a href="https://en.wikipedia.org/wiki/Stochastic" style="color: #EDE379"><i>stochastic</i></a> 
        <a href="https://en.wikipedia.org/wiki/Streaming_algorithm" style="color: #EDE379"><i>streaming algorithms</i></a></p>
      <p class="lead" style="font-size: 18px; line-height: 1.0; margin-bottom: 15px; color: #FFFFFF"><i>"A truly excellent example of theoretically-informed algorithm engineering"</i> -- Graham Cormode</p>
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<p><b>The Business Challenge:</b> Analyzing Big Data Quickly.</p>
<p>In the analysis of big data there are often problem queries that don’t scale because they require huge compute resources and time to generate exact results. Examples include <i>count distinct</i>, quantiles, most-frequent items, joins, matrix computations, and graph analysis.</p>

<p>If approximate results are acceptable, there is a class of specialized algorithms, called streaming algorithms, or <a href="/docs/Background/SketchOrigins.html">sketches</a> that can produce results orders-of magnitude faster and with mathematically proven error bounds. For interactive queries there may not be other viable alternatives, and in the case of real-time analysis, sketches are the only known solution.</p>

<p>For any system that needs to extract useful information from big data these sketches are a required toolkit that should be tightly integrated into their analysis capabilities. This technology has helped Yahoo successfully reduce data processing times from days or hours to minutes or seconds on a number of its internal platforms.</p>

<p>This project is dedicated to providing a broad selection of sketch algorithms of production quality. Contributions are welcome from those interested in further development of this science and art.</p>
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      <a href="/docs/Architecture/LargeScale.html#speed">
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        <h2>Fast</h2>
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      <p class="text-justify"><a href="/docs/Background/SketchOrigins.html">Sketches</a> are <i>fast</i>. 
      The sketch algorithms in this library process data in a single pass and are suitable for 
      both real-time and batch. 
      Sketches enable streaming computation of set expression cardinalities, quantiles, frequency estimation and more. 
      In addition, designing a system around sketching allows simplification of system's architecture and reduction in overall compute resources required for these heretofore difficult computational tasks.</p>
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      <a href="/docs/Architecture/LargeScale.html#specific-sketch-features-for-large-data">
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        <h2>Big Data</h2>
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      <p class="text-justify">This library has been specifically designed for production systems that must process massive data. 
      The library includes adaptors for Apache Hive, Apache Pig, and PostgreSQL (C++). These adaptors also stand as examples for adaptors for other systems. 
      The sketches in this library are designed to have compatible binary representations across languages (Java, C++, Python) and platforms.
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        <h2>Analysis</h2>
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      <p class="text-justify">Built-in Theta Sketch set operators (Union, Intersection, Difference) 
      produce sketches as a result (and not just a number) enabling full set expressions of cardinality, 
      such as ((A &#8746; B) &#8745; (C &#8746; D)) \ (E &#8746; F). 
      This capability along with predictable and superior accuracy 
      (compared with <i>Include/Exclude</i> approaches) enable unprecedented analysis capabilities 
      for fast queries. </p>
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