2018-02-23 01:43:24 -05:00
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<title>CSE 4/562 - Spring 2018</title>
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<div class="header">
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<!-- Any Talk-Specific Header Content Goes Here -->
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CSE 4/562 - Database Systems
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</div>
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<div class="slides">
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<section>
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<h1>Indexes</h1>
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<h3>CSE 4/562 – Database Systems</h3>
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2018-02-23 15:58:01 -05:00
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<h5>February 23, 2018</h5>
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2018-02-23 01:43:24 -05:00
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</section>
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<section>
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<section>
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<h3>Recap</h3>
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</section>
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<section>
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<div style="display: inline-block; margin-right: 100px;">
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<h3>Index</h3>
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<img src="graphics/2018-02-23-Index.png" height="300px" />
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</div>
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<div style="display: inline-block;">
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<h3>Data</h3>
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<img src="graphics/2018-02-23-Data.png" height="300px" />
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</div>
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</section>
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<section>
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<p>Data, even if well organized still requires you to page through a lot.</p>
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<p>An index helps you quickly jump to specific data you might be interested in.</p>
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</section>
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<section>
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<h3>Data Organization</h3>
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<dl>
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<div class="fragment">
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<dt>Unordered Heap</dt>
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<dd>No organization at all. $O(N)$ reads.</dd>
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</div>
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<div class="fragment">
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<dt>(Secondary) Index</dt>
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<dd>Index structure over unorganized data. $O(\ll N)$ <b>random</b> reads for <b>some</b> queries.</dd>
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</div>
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<div class="fragment">
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<dt>Clustered (Primary) Index</dt>
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<dd>Index structure over clustered data. $O(\ll N)$ <b>sequential</b> reads for <b>some</b> queries.</dd>
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</div>
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</dl>
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</section>
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</section>
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<section>
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<section>
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<h3>Hash Indexes</h3>
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<p style="margin-top: 100px; text-align: left;">
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A hash function $h(k)$ is ...
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<dl>
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<dt>... deterministic</dt>
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<dd>The same $k$ always produces the same hash value.</dd>
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<dt>... (pseudo-)random</dt>
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<dd>Different $k$s are unlikely to have the same hash value.</dd>
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</dl>
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</p>
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<p class="fragment">Modulus $h(k)\%N$ gives you a random number in $[0, N)$</p>
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</section>
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<section>
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<svg data-src="graphics/2018-02-23-HashTable.svg" class="stretch"/>
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</section>
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<section>
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<h3>Problems</h3>
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<dl>
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<dt>$N$ is too small</dt>
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<dd>Too many overflow pages (slower reads).</dd>
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<dt>$N$ is too big</dt>
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<dd>Too many normal pages (wasted space).</dd>
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</dl>
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</section>
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<section>
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<p><b>Idea:</b> Resize the structure as needed</p>
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</section>
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<section>
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<p>To keep things simple, let's use $$h(k) = k$$</p>
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<p class="fragment" style="font-size: 70%">(you wouldn't actually do this in practice)</p>
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</section>
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<section>
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<svg data-src="graphics/2018-02-23-HashResize-Naive.svg" class="stretch"/>
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</section>
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<section>
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<h3>Problems</h3>
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<dl>
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<dt class="fragment" data-fragment-index="1">Changing hash functions reallocates everything</dt>
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<dd class="fragment" data-fragment-index="1">Only double/halve the size of a hash function</dd>
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<dt class="fragment" data-fragment-index="2">Changing sizes still requires reading everything</dt>
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<dd class="fragment" data-fragment-index="3"><b>Idea:</b> Only redistribute buckets that are too big</dd>
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</dl>
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</section>
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<section>
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<svg data-src="graphics/2018-02-23-HashResize-Dynamic.svg" class="stretch" />
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</section>
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<section>
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<h3>Dynamic Hashing</h3>
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<ul>
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<li>Add a level of indirection (Directory).</li>
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<li>A data page $i$ can store data with $h(k)%2^n=i$ for any $n$.</li>
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<li>Double the size of the directory (almost free) by duplicating existing entries.</li>
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<li>When bucket $i$ fills up, split on the next power of 2.</li>
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<li>Can also merge buckets/halve the directory size. </li>
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</ul>
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</section>
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</section>
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<section>
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<section>
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<h3>CDF-Based Indexing</h3>
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<p class="fragment" style="margin-top: 100px;"><b>"The Case for Learned Index Structures"</b><br/>by Kraska, Beutel, Chi, Dean, Polyzotis</p>
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</section>
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<section>
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<svg data-src="graphics/2018-02-23-CDF-Linear.svg"/>
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</section>
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<section>
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<svg data-src="graphics/2018-02-23-CDF-LinearApprox.svg"/>
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</section>
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<section>
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<h3>Cumulative Distribution Function (CDF)</h3>
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<img src="graphics/2018-02-23-CDF-Plot.png" />
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<p>$f(key) \mapsto position$</p>
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<p class="fragment" style="font-size: 50%">(not exactly true, but close enough for today)</p>
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</section>
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<section>
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<h3>Using CDFs to find records</h3>
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<dl>
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<dt>Ideal: $f(k) = position$</dt>
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<dd>$f$ encodes the <b>exact</b> location of a record</dd>
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<dt class="fragment">Ok: $f(k) \approx position$ <span class="fragment">($\left|f(k) - position\right| < \epsilon$)</span></dt>
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<dd class="fragment">$f$ gets you to within $\epsilon$ of the key</dd>
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<dd class="fragment">Only need local search on one (or so) leaf pages.</dd>
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</dl>
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<p class="fragment"><b>Simplified Use Case:</b> Static data with "infinite" prep time.</p>
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</section>
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<section>
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<h3>How to define $f$?</h3>
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<ul>
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<li class="fragment">Linear ($f(k) = a\cdot k + b$)</li>
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<li class="fragment">Polynomial ($f(k) = a\cdot k + b \cdot k^2 + \ldots$)</li>
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<li class="fragment">Neural Network ($f(k) = $<img src="graphics/Clipart/magic-wand.png" height="100px" style="vertical-align: middle;">)</li>
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</ul>
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</section>
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<section>
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<p>We have infinite prep time, so fit a (tiny) neural network to the CDF.</p>
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</section>
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<section>
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<h3>Neural Networks</h3>
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<ul>
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<dt class="fragment" data-fragment-index="1">Extremely Generalized Regression</dt>
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<dd class="fragment" data-fragment-index="1">Essentially a really really really complex, fittable function with a lot of parameters.</dd>
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<dt class="fragment" data-fragment-index="2">Captures Nonlinearities</dt>
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<dd class="fragment" data-fragment-index="2">Most regressions can't handle discontinuous functions, which many key spaces have.</dd>
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<dt class="fragment" data-fragment-index="3">No Branching</dt>
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<dd class="fragment" data-fragment-index="3"><code>if</code> statements are <b>really</b> expensive on modern processors.</dd>
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<dd class="fragment" data-fragment-index="4">(Compare to B+Trees with $\log_2 N$ if statements)</dd>
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</ul>
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</section>
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<section>
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<h3>Summary</h3>
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<dl>
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<dt>Tree Indexes</dt>
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<dd>$O(\log N)$ access, supports range queries, easy size changes.</dd>
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<dt>Hash Indexes</dt>
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<dd>$O(1)$ access, doesn't change size efficiently, only equality tests.</dd>
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<dt>CDF Indexes</dt>
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<dd>$O(1)$ access, supports range queries, static data only.</dd>
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</dl>
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</section>
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</section>
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<section>
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<p><b>Next Class:</b> Using Indexes</p>
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</section>
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</div></div>
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<script src="../reveal.js-3.6.0/js/reveal.js"></script>
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<script>
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// Full list of configuration options available at:
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// https://github.com/hakimel/../reveal.js#configuration
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Reveal.initialize({
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2018-02-26 19:44:30 -05:00
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controls: true,
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2018-02-23 01:43:24 -05:00
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progress: true,
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history: true,
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slideNumber: true,
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transition: 'fade', // none/fade/slide/convex/concave/zoom
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chart: {
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gridLines: { color: "#333", zeroLineColor: "#333" },
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ticks: { fontColor: "#333", fontSize: 16 },
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}
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},
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line: { borderColor: [ "rgba(20,220,220,.8)" , "rgba(220,120,120,.8)", "rgba(20,120,220,.8)" ], "borderDash": [ [5,10], [0,0] ]},
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bar: { backgroundColor: [
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"rgba(220,220,220,0.8)",
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"rgba(151,187,205,0.8)",
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"rgba(205,151,187,0.8)",
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"rgba(187,205,151,0.8)"
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]
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},
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pie: { backgroundColor: [ ["rgba(0,0,0,.8)" , "rgba(220,20,20,.8)", "rgba(20,220,20,.8)", "rgba(220,220,20,.8)", "rgba(20,20,220,.8)"] ]},
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radar: { borderColor: [ "rgba(20,220,220,.8)" , "rgba(220,120,120,.8)", "rgba(20,120,220,.8)" ]},
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},
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// Optional ../reveal.js plugins
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dependencies: [
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{ src: '../reveal.js-3.6.0/lib/js/classList.js', condition: function() { return !document.body.classList; } },
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{ src: '../reveal.js-3.6.0/plugin/math/math.js',
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condition: function() { return true; },
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mathjax: '../reveal.js-3.6.0/js/MathJax.js'
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},
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{ src: '../reveal.js-3.6.0/plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
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{ src: '../reveal.js-3.6.0/plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
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{ src: '../reveal.js-3.6.0/plugin/highlight/highlight.js', async: true, condition: function() { return !!document.querySelector( 'pre code' ); }, callback: function() { hljs.initHighlightingOnLoad(); } },
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{ src: '../reveal.js-3.6.0/plugin/zoom-js/zoom.js', async: true },
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{ src: '../reveal.js-3.6.0/plugin/notes/notes.js', async: true },
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// Chart.min.js
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{ src: '../reveal.js-3.6.0/plugin/chart/Chart.min.js'},
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// the plugin
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{ src: '../reveal.js-3.6.0/plugin/chart/csv2chart.js'},
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{ src: '../reveal.js-3.6.0/plugin/svginline/es6-promise.auto.js', async: false },
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{ src: '../reveal.js-3.6.0/plugin/svginline/data-src-svg.js', async: false }
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]
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});
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</script>
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</body>
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</html>
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