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@ -4,6 +4,21 @@ title: "Query Evaluation"
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date: February 11, 2019
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textbook: "Ch. 15.1-15.5, 16.7"
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---
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<!-- 2019 by OK:
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The discussion of accounting needs to be augmented a little bit.
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Specifically, something that's still not coming across for some students is the idea of counting only the number of IOs *added*.
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An example comparing the cost of individual sub-plans to the overall plan might help.
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For example, draw out the full query plan, highlight the subplan, count its cost, then compute the total cost of the entire plan, and repeat.
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e.g., after introducing select, show that adding more select operators doesn't add more IOs or memory to the plan.
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More similar examples with Union and Cross would also help.
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Might help to tighten up the time spent a little too. I had to cut out before introducing Sort-Merge Joins
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-->
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<section>
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<section>
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<h3>Query Evaluation Styles</h3>
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@ -130,19 +145,19 @@ textbook: "Ch. 15.1-15.5, 16.7"
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<dd class="fragment">Constant!</dd>
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<dt>IOs added?</dt>
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<dd class="fragment">$|S| \cdot \texttt{cost}(R)$ tuples read</dd>
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<dd class="fragment">(or $|R| \cdot \texttt{cost}(S)$)</dd>
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<dd class="fragment">$(|R|-1) \cdot \texttt{cost}(S)$ tuples read</dd>
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<dd class="fragment">(or $(|S|-1) \cdot \texttt{cost}(R)$)</dd>
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</dl>
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<p class="fragment">If $R$ is a query, this can be very expensive</p>
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<p class="fragment">If $S$ is a query, this can get very expensive</p>
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</section>
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<section>
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<h3>Cross ($R \times S$)</h3>
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<p><b>Optimization 1: </b> Cache $R$ in memory</p>
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<p><b>Optimization 1: </b> Cache $S$ in memory</p>
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<dl>
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<dt>Memory Required?</dt>
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<dd class="fragment">$O(|R|)$</dd>
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<dd class="fragment">$O(|S|)$</dd>
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<dt>IOs added?</dt>
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<dd class="fragment">None!</dd>
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@ -151,15 +166,15 @@ textbook: "Ch. 15.1-15.5, 16.7"
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<section>
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<h3>Cross ($R \times S$)</h3>
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<p><b>Optimization 2: </b> Cache $R$ on disk</p>
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<p><b>Optimization 2: </b> Cache $S$ on disk</p>
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<dl>
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<dt>Memory Required?</dt>
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<dd class="fragment">Constant</dd>
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<dt>IOs added?</dt>
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<dd class="fragment">$|R|$ tuples written.</dd>
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<dd class="fragment">$(|S| - 1) \cdot |R|$ tuples read.</dd>
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<dd class="fragment">$|S|$ tuples written.</dd>
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<dd class="fragment">$(|R| - 1) \cdot |R|$ tuples read.</dd>
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</dl>
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</section>
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@ -207,15 +222,16 @@ textbook: "Ch. 15.1-15.5, 16.7"
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<section>
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<h3>Block-Nested Loop ($R \times S$)</h3>
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<p>(with $\mathcal B$ as the block size for $S$)</p>
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<p>(with $\mathcal B$ as the block size for $R$)</p>
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<p>(and with caching $S$ to disk)</p>
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<dl>
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<dt>Memory Required?</dt>
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<dd class="fragment">$O(\mathcal B)$</dd>
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<dt>IOs added?</dt>
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<dd class="fragment">$|R|$ tuples written.</dd>
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<dd class="fragment">$(\frac{|S|}{\mathcal B} - 1) \cdot |R|$ tuples read.</dd>
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<dd class="fragment">$|S|$ tuples written.</dd>
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<dd class="fragment">$(\frac{|R|}{\mathcal B} - 1) \cdot |R|$ tuples read.</dd>
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</dl>
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<p style="font-size: 70%;" class="fragment">In-memory caching is a special case of block-nested loop with $\mathcal B = |S|$</p>
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<p style="font-size: 70%;" class="fragment">Does the block size for $R$ matter?</p>
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@ -1,362 +1,512 @@
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<!doctype html>
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<html lang="en">
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<head>
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<meta charset="utf-8">
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<title>CSE 4/562 - Spring 2018</title>
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<meta name="description" content="CSE 4/562 - Spring 2018">
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<meta name="author" content="Oliver Kennedy">
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<body>
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<div class="reveal">
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<!-- Any section element inside of this container is displayed as a slide -->
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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>Extended RA</h1>
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<h3>CSE 4/562 – Database Systems</h3>
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<h5>February 12, 2018</h5>
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</section>
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<section>
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<section>
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<h3>Extended Relational Algebra</h3>
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<dl>
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<dt class="fragment highlight-grey" data-fragment-index="1">Set/Bag Operations</dt>
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<dd class="fragment highlight-grey" data-fragment-index="1">Select ($\sigma$), Project ($\pi$), Join ($\bowtie$), Union ($\cup$)</dd>
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<dt>Bag Operations</dt>
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<dd>Distinct ($\delta$), Outer Joins (⟗)</dd>
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<dt>List Operations</dt>
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<dd>Sort ($\tau$), Limit</dd>
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<dt>Arithmetic Operations</dt>
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<dd>Extended Projection ($\pi$), Aggregation ($\sigma$), Grouping ($\gamma$)</dd>
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</dl>
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<dl>
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</dl>
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</section>
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<section>
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<h3>Extended Projection</h3>
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<p style="margin: 50px;">Like normal projection, but can create new columns</p>
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$\pi_{M \leftarrow A+B*C,\; N \leftarrow 2}(R)$
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<p>produces 1 row for every row of R, with 2 columns: M and N</p>
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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>Outer Join</h3>
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<p class="fragment">... but first</p>
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</section>
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<section>
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<h3><code>NULL</code> Values</h3>
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<ul>
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<li>Field values can be unknown or inapplicable.<ul>
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<li>A tree with an unknown species.</li>
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<li>The street of a tree in a park.</li>
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<li>The '.' on many of your ID cards</li>
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</ul></li>
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<li>SQL provides a special <code>NULL</code> value for these cases</li>
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</ul>
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<p class="fragment">NULL makes things more complicated.</p>
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</section>
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<section>
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$$\textbf{Trees.SPC_COMMON} = \texttt{'Brooklyn'}$$
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<p style="margin: 50px;" class="fragment">
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What happens if <b>Trees.SPC_COMMON</b> is NULL?
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</p>
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<div class="fragment">
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$$\texttt{NULL} = \textbf{'Brooklyn'} \equiv \textbf{Unknown}$$
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</div>
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</section>
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<section>
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<table>
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<tr><td>Unknown</td><td>AND</td><td>Unknown</td><td>$\equiv$</td><td>Unknown</td></tr>
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<tr><td>Unknown</td><td>AND</td><td>True</td><td>$\equiv$</td><td>Unknown</td></tr>
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<tr><td>Unknown</td><td>AND</td><td>False</td><td>$\equiv$</td><td>False</td></tr>
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<tr><td colspan="5"></td></tr>
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<tr><td>Unknown</td><td>OR</td><td>Unknown</td><td>$\equiv$</td><td>Unknown</td></tr>
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<tr><td>Unknown</td><td>OR</td><td>True</td><td>$\equiv$</td><td>True</td></tr>
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<tr><td>Unknown</td><td>OR</td><td>False</td><td>$\equiv$</td><td>Unknown</td></tr>
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<tr><td colspan="5"></td></tr>
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<tr><td></td><td>NOT</td><td>Unknown</td><td>$\equiv$</td><td>Unknown</td></tr>
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</table>
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<p class="fragment"><code>WHERE</code> clauses eliminate all non-True rows</p>
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</section>
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<section>
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$$Streets \bowtie_{StreetName} Trees$$
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<p style="margin-top: 100px;" class="fragment">What happens if some streets have no trees?</p>
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</section>
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<section>
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<h3>Outer Join (⟗, ⟕, ⟖)</h3>
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<ol>
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<li>Include all results from the normal (inner) join.</li>
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<li>Also include rows that don't get joined.</li>
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</ol>
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</section>
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<section>
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<h3>Outer Join</h3>
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<dl>
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<dt>Inner Join</dt>
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<dd>Normal, plain, simple join</dd>
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<dt>Left Outer Join (⟕)</dt>
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<dd>Include un-joined rows from the left hand side</dd>
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<dt>Right Outer Join (⟖)</dt>
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<dd>Include un-joined rows from the right hand side</dd>
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<dt>[Full] Outer Join (⟗)</dt>
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<dd>Include un-joined rows from either side</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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<section>
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<h3>Sort / Limit</h3>
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<p>
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$$\tau_{A}(R)$$
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The tuples of $R$ in ascending order according to 'A'
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</p>
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<p>
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$$\textbf{L}_{n}(R)$$
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The first $n$ tuples of R
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<div style="font-size: 60%">(Typically combined with sort. If not, pick arbitrarily.)</div>
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</p>
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</section>
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<section>
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<h3>Sort</h3>
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<p style="margin-top: 100px;">
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Pick your favorite sort algorithm.
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</p>
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<p class="fragment">What happens if you don't have enough memory?</p>
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</section>
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<section>
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<p><b>Key Idea:</b> Merging 2 sorted lists requires $O(1)$ memory.</p>
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</section>
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<section>
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<h3>2-Way Sort</h3>
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<dl>
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<dt>Pass 1</dt>
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<dd>Create lots of (small) sorted lists.</dd>
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<dt>Pass 2+</dt>
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<dd>Merge sorted lists of size $N$ into sorted lists of size $2N$</dd>
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</dl>
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</section>
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<section>
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<h3>Pass 1: Create Sorted Runs</h3>
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<svg data-src="graphics/2018-02-14-Sort-Run.svg" style="margin: 100px;" />
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</section>
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<section>
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<h3>Pass 2: Merge Sorted Runs</h3>
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<svg data-src="graphics/2018-02-14-Merge-Run.svg" style="margin: 100px;" />
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</section>
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<section>
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<p>Repeat Pass 2 As Needed.</p>
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</section>
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<section>
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<p>What's the bottleneck?</p>
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<p class="fragment">IO Cost: $O(N \cdot \lceil\log_2(N)\rceil)$<br/>(with $N$ blocks)</p>
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</section>
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<section>
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<svg data-src="graphics/2018-02-14-Merge-Tree.svg" />
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</section>
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<section>
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<h3>Using More Memory</h3>
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<dl>
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<dt>Pass 1</dt>
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<dd>Sort Bigger Buffers</dd>
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<dd class="fragment">Re-Use Memory When Done</dd>
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<dt>Pass 2</dt>
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<dd>Merge $K$ Runs Simultaneously: $O(N \cdot \lceil\log_K(N)\rceil)$ IO</dd>
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</dl>
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-1.svg" />
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-2.svg" />
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-3.svg" />
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-4.svg" />
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-5.svg" />
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-6.svg" />
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-7.svg" />
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</section>
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<section>
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<h3>Replacement Sort</h3>
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<img src="graphics/2018-02-14-ReplSort-8.svg" />
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</section>
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<section>
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<p>On average, we'll get runs of size $2 \cdot |WS|$</p>
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</section>
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</section>
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</div></div>
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{ src: '../reveal.js-3.6.0/plugin/chart/csv2chart.js'},
|
||||
{ src: '../reveal.js-3.6.0/plugin/svginline/es6-promise.auto.js', async: false },
|
||||
{ src: '../reveal.js-3.6.0/plugin/svginline/data-src-svg.js', async: false }
|
||||
]
|
||||
});
|
||||
|
||||
</script>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
---
|
||||
template: templates/cse4562_2019_slides.erb
|
||||
title: "Extended Relational Algebra"
|
||||
date: February 13, 2019
|
||||
textbook: "Ch. 5.2, 15.4"
|
||||
---
|
||||
<section>
|
||||
<section>
|
||||
<h3>Extended Relational Algebra</h3>
|
||||
|
||||
<dl>
|
||||
<dt class="fragment highlight-grey" data-fragment-index="1">Set/Bag Operations</dt>
|
||||
<dd class="fragment highlight-grey" data-fragment-index="1">Select ($\sigma$), Project ($\pi$), Join ($\bowtie$), Union ($\cup$)</dd>
|
||||
|
||||
<dt>Bag Operations</dt>
|
||||
<dd>Distinct ($\delta$), Outer Joins (⟗)</dd>
|
||||
|
||||
<dt>List Operations</dt>
|
||||
<dd>Sort ($\tau$), Limit (L)</dd>
|
||||
|
||||
<dt>Arithmetic Operations</dt>
|
||||
<dd>Extended Projection ($\pi$), Aggregation ($\sigma$), Grouping ($\gamma$)</dd>
|
||||
</dl>
|
||||
|
||||
<dl>
|
||||
|
||||
</dl>
|
||||
</section>
|
||||
<section>
|
||||
<h3>Extended Projection</h3>
|
||||
|
||||
<p style="margin: 50px;">Like normal projection, but can create new columns</p>
|
||||
|
||||
$\pi_{M \leftarrow A+B*C,\; N \leftarrow 2}(R)$
|
||||
<p>produces 1 row for every row of R, with 2 columns: M and N</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Outer Join</h3>
|
||||
<p class="fragment">... but first</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3><code>NULL</code> Values</h3>
|
||||
|
||||
<ul>
|
||||
<li>Field values can be unknown or inapplicable.<ul>
|
||||
<li>A tree with an unknown species.</li>
|
||||
<li>The street of a tree in a park.</li>
|
||||
<li>The '.' on many of your ID cards</li>
|
||||
</ul></li>
|
||||
<li>SQL provides a special <code>NULL</code> value for these cases</li>
|
||||
</ul>
|
||||
<p class="fragment">NULL makes things more complicated.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
$$\textbf{Trees.SPC_COMMON} = \texttt{'Brooklyn'}$$
|
||||
|
||||
<p style="margin: 50px;" class="fragment">
|
||||
What happens if <b>Trees.SPC_COMMON</b> is NULL?
|
||||
</p>
|
||||
|
||||
<div class="fragment">
|
||||
$$\texttt{NULL} = \textbf{'Brooklyn'} \equiv \textbf{Unknown}$$
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><td>Unknown</td><td>AND</td><td>Unknown</td><td>$\equiv$</td><td>Unknown</td></tr>
|
||||
<tr class="fragment" data-fragment-index="1"><td>Unknown</td><td>AND</td><td>True</td><td>$\equiv$</td><td>Unknown</td></tr>
|
||||
<tr class="fragment" data-fragment-index="2"><td>Unknown</td><td>AND</td><td>False</td><td>$\equiv$</td><td>False</td></tr>
|
||||
<tr><td colspan="5"></td></tr>
|
||||
<tr class="fragment" data-fragment-index="3"><td>Unknown</td><td>OR</td><td>Unknown</td><td>$\equiv$</td><td>Unknown</td></tr>
|
||||
<tr class="fragment" data-fragment-index="3"><td>Unknown</td><td>OR</td><td>True</td><td>$\equiv$</td><td>True</td></tr>
|
||||
<tr class="fragment" data-fragment-index="3"><td>Unknown</td><td>OR</td><td>False</td><td>$\equiv$</td><td>Unknown</td></tr>
|
||||
<tr><td colspan="5"></td></tr>
|
||||
<tr class="fragment" data-fragment-index="4"><td></td><td>NOT</td><td>Unknown</td><td>$\equiv$</td><td>Unknown</td></tr>
|
||||
</table>
|
||||
|
||||
<p class="fragment"><code>WHERE</code> clauses eliminate all non-True rows</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
$$Streets \bowtie_{StreetName} Trees$$
|
||||
|
||||
<p style="margin-top: 100px;" class="fragment">What happens if some streets have no trees?</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Outer Join (⟗, ⟕, ⟖)</h3>
|
||||
|
||||
<ol>
|
||||
<li>Include all results from the normal (inner) join.</li>
|
||||
<li>Also include rows that don't get joined.</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Outer Join</h3>
|
||||
|
||||
<dl>
|
||||
<dt>Inner Join</dt>
|
||||
<dd>Normal, plain, simple join</dd>
|
||||
|
||||
<dt>Left Outer Join (⟕)</dt>
|
||||
<dd>Include un-joined rows from the left hand side</dd>
|
||||
|
||||
<dt>Right Outer Join (⟖)</dt>
|
||||
<dd>Include un-joined rows from the right hand side</dd>
|
||||
|
||||
<dt>[Full] Outer Join (⟗)</dt>
|
||||
<dd>Include un-joined rows from either side</dd>
|
||||
</dl>
|
||||
</section>
|
||||
<section>
|
||||
<div style="display: inline-block; margin-right: 50px;">
|
||||
<p style="text-decoration: underline;">Streets</p>
|
||||
<table>
|
||||
<tr><th>District</th><th>StreetName</th></tr>
|
||||
<tr><td>A</td><td>Apple St.</td></tr>
|
||||
<tr><td>B</td><td>Border St.</td></tr>
|
||||
<tr><td>C</td><td>Coventry St.</td></tr>
|
||||
<tr><td>D</td><td>Durham St.</td></tr>
|
||||
</table>
|
||||
</div>
|
||||
<div style="display: inline-block;">
|
||||
<p style="text-decoration: underline;">Trees</p>
|
||||
<table>
|
||||
<tr><th>TreeId</th><th>StreetName</th></tr>
|
||||
<tr><td>1</td><td>Apple St.</td></tr>
|
||||
<tr><td>2</td><td>Border St.</td></tr>
|
||||
<tr><td>3</td><td>Durham St.</td></tr>
|
||||
<tr><td>4</td><td>Elicott St.</td></tr>
|
||||
</table>
|
||||
</div>
|
||||
</section>
|
||||
<section>
|
||||
<p style="text-decoration: underline;">Streets ⟗ Trees</p>
|
||||
<table>
|
||||
<tr><th>District</th><th>StreetName</th> <th>TreeId</th><th>StreetName</th></tr>
|
||||
<tr><td>A</td> <td>Apple St.</td> <td>1</td> <td>Apple St.</td></tr>
|
||||
<tr><td>B</td> <td>Border St.</td> <td>2</td> <td>Border St.</td></tr>
|
||||
<tr class="fragment highlight-red" data-fragment-index="1"><td>C</td> <td>Coventry St.</td><td>NULL</td> <td>NULL</td></tr>
|
||||
<tr><td>D</td> <td>Durham St.</td> <td>3</td> <td>Durham St.</td></tr>
|
||||
<tr class="fragment highlight-blue" data-fragment-index="2"><td>NULL</td> <td>NULL</td> <td>4</td> <td>Elicott St.</td></tr>
|
||||
</table>
|
||||
<p class="fragment" data-fragment-index="1" style="color: red;">Only LEFT outer join</p>
|
||||
<p class="fragment" data-fragment-index="2" style="color: blue;">Only RIGHT outer join</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Sort / Limit</h3>
|
||||
|
||||
<p>
|
||||
$$\tau_{A}(R)$$
|
||||
The tuples of $R$ in ascending order according to 'A'
|
||||
</p>
|
||||
|
||||
<p>
|
||||
$$\textbf{L}_{n}(R)$$
|
||||
The first $n$ tuples of R
|
||||
<div style="font-size: 60%">(Typically combined with sort. If not, pick arbitrarily.)</div>
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Sort</h3>
|
||||
|
||||
<p style="margin-top: 100px;">
|
||||
Pick your favorite sort algorithm.
|
||||
</p>
|
||||
|
||||
<p class="fragment">What happens if you don't have enough memory?</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Key Idea:</b> Merging 2 sorted lists requires $O(1)$ memory.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>2-Way Sort</h3>
|
||||
<dl>
|
||||
<dt>Pass 1</dt>
|
||||
<dd>Create lots of (small) sorted lists.</dd>
|
||||
|
||||
<dt>Pass 2+</dt>
|
||||
<dd>Merge sorted lists of size $N$ into sorted lists of size $2N$</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Pass 1: Create Sorted Runs</h3>
|
||||
<svg data-src="graphics/2018-02-14-Sort-Run.svg" style="margin: 100px;" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Pass 2: Merge Sorted Runs</h3>
|
||||
<svg data-src="graphics/2018-02-14-Merge-Run.svg" style="margin: 100px;" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Repeat Pass 2 As Needed.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>What's the bottleneck?</p>
|
||||
|
||||
<p class="fragment">IO Cost: $O(N \cdot \lceil\log_2(N)\rceil)$<br/>(with $N$ blocks)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<svg data-src="graphics/2018-02-14-Merge-Tree.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Using More Memory</h3>
|
||||
|
||||
<dl>
|
||||
<dt>Pass 1</dt>
|
||||
<dd>Sort Bigger Buffers</dd>
|
||||
<dd class="fragment">Re-Use Memory When Done</dd>
|
||||
|
||||
<dt>Pass 2</dt>
|
||||
<dd>Merge $K$ Runs Simultaneously: $O(N \cdot \lceil\log_K(N)\rceil)$ IO</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-1.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-2.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-3.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-4.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-5.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-6.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-7.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Replacement Sort</h3>
|
||||
<img src="graphics/2018-02-14-ReplSort-8.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>On average, we'll get runs of size $2 \cdot |WS|$</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Aggregation</h3>
|
||||
|
||||
<dl>
|
||||
<div class="fragment">
|
||||
<dt>Normal Aggregates</dt>
|
||||
<dd><code class="sql">SELECT COUNT(*) FROM R</code></dd>
|
||||
<dd><code class="sql">SELECT SUM(A) FROM R</code></dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Group-By Aggregates</dt>
|
||||
<dd><code class="sql">SELECT A, SUM(B) FROM R GROUP BY A</code></dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Distinct</dt>
|
||||
<dd><code class="sql">SELECT DISTINCT A FROM R</code></dd>
|
||||
<dd class="fragment"><code class="sql">SELECT A FROM R GROUP BY A</code></dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Normal Aggregates</h3>
|
||||
|
||||
<table style="font-size: 80%;" class="fragment">
|
||||
<tr><th>TREE_ID</th><th>SPC_COMMON</th><th>BORONAME</th><th>TREE_DBH</th></tr>
|
||||
<tr><td>180683</td><td>'red maple'</td><td>'Queens'</td><td>3</td></tr>
|
||||
<tr><td>315986</td><td>'pin oak'</td><td>'Queens'</td><td>21</td></tr>
|
||||
<tr><td>204026</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>3</td></tr>
|
||||
<tr><td>204337</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>10</td></tr>
|
||||
<tr><td>189565</td><td>'American linden'</td><td>'Brooklyn'</td><td>21</td></tr>
|
||||
<tr><td style="font-weight: bold;" colspan="3">... and 683783 more</td></tr>
|
||||
</table>
|
||||
|
||||
<div style="margin-top: 60px">
|
||||
<code class="sql fragment">SELECT COUNT(*) FROM TREES</code>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table style="font-size: 70%;">
|
||||
<tr><th>TREE_ID</th><th>SPC_COMMON</th><th>BORONAME</th><th>TREE_DBH</th></tr>
|
||||
<tr class="fragment" data-fragment-index="1"><td colspan="4">COUNT = 0</td></tr>
|
||||
<tr class="fragment" data-fragment-index="2" style="font-size: smaller;"><td>180683</td><td>'red maple'</td><td>'Queens'</td><td>3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="3"><td colspan="4">COUNT = 1</td></tr>
|
||||
<tr class="fragment" data-fragment-index="4" style="font-size: smaller;"><td>315986</td><td>'pin oak'</td><td>'Queens'</td><td>21</td></tr>
|
||||
<tr class="fragment" data-fragment-index="5"><td colspan="4">COUNT = 2</td></tr>
|
||||
<tr class="fragment" data-fragment-index="6" style="font-size: smaller;"><td>204026</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="6"><td colspan="4">COUNT = 3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="7" style="font-size: smaller;"><td>204337</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>10</td></tr>
|
||||
<tr class="fragment" data-fragment-index="7"><td colspan="4">COUNT = 4</td></tr>
|
||||
<tr class="fragment" data-fragment-index="8" style="font-size: smaller;"><td>189565</td><td>'American linden'</td><td>'Brooklyn'</td><td>21</td></tr>
|
||||
<tr class="fragment" data-fragment-index="8"><td colspan="4">COUNT = 5</td></tr>
|
||||
<tr class="fragment" data-fragment-index="9"><td style="font-weight: bold;" colspan="3">... and 683783 more</td></tr>
|
||||
<tr class="fragment" data-fragment-index="9"><td colspan="4">COUNT = 683788</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<div style="margin-bottom: 60px">
|
||||
<code class="sql">SELECT SUM(TREE_DBH) FROM TREES</code>
|
||||
</div>
|
||||
<table style="font-size: 70%;">
|
||||
<tr><th>TREE_ID</th><th>SPC_COMMON</th><th>BORONAME</th><th>TREE_DBH</th></tr>
|
||||
<tr class="fragment" data-fragment-index="1"><td colspan="4">SUM = 0</td></tr>
|
||||
<tr class="fragment" data-fragment-index="2" style="font-size: smaller;"><td>180683</td><td>'red maple'</td><td>'Queens'</td><td>3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="3"><td colspan="4">SUM = 3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="4" style="font-size: smaller;"><td>315986</td><td>'pin oak'</td><td>'Queens'</td><td>21</td></tr>
|
||||
<tr class="fragment" data-fragment-index="5"><td colspan="4">SUM = 24</td></tr>
|
||||
<tr class="fragment" data-fragment-index="6" style="font-size: smaller;"><td>204026</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="6"><td colspan="4">SUM = 27</td></tr>
|
||||
<tr class="fragment" data-fragment-index="7" style="font-size: smaller;"><td>204337</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>10</td></tr>
|
||||
<tr class="fragment" data-fragment-index="7"><td colspan="4">SUM = 37</td></tr>
|
||||
<tr class="fragment" data-fragment-index="8" style="font-size: smaller;"><td>189565</td><td>'American linden'</td><td>'Brooklyn'</td><td>21</td></tr>
|
||||
<tr class="fragment" data-fragment-index="8"><td colspan="4">SUM = 58</td></tr>
|
||||
<tr class="fragment" data-fragment-index="9"><td style="font-weight: bold;" colspan="3">... and 683783 more</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Basic Aggregate Pattern</h3>
|
||||
<p class="fragment" style="font-size: 70%">This is also sometimes called a "fold"</p>
|
||||
<dl>
|
||||
<dt>Init</dt>
|
||||
<dd>Define a starting value for the accumulator</dd>
|
||||
<dt>Fold(Accum, New)</dt>
|
||||
<dd>Merge a new value into the accumulator</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>COUNT(*)</h3>
|
||||
<dl>
|
||||
<dt>Init</dt>
|
||||
<dd class="fragment">$0$</dd>
|
||||
<dt>Fold(Accum, New)</dt>
|
||||
<dd class="fragment">$Accum + 1$</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>SUM(A)</h3>
|
||||
<dl>
|
||||
<dt>Init</dt>
|
||||
<dd class="fragment">$0$</dd>
|
||||
<dt>Fold(Accum, New)</dt>
|
||||
<dd class="fragment">$Accum + New$</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>AVG(A)</h3>
|
||||
<dl>
|
||||
<dt>Init</dt>
|
||||
<dd class="fragment">$\{ sum = 0, count = 0 \}$</dd>
|
||||
<dt>Fold(Accum, New)</dt>
|
||||
<dd class="fragment">$\{ sum = Accum.sum + New, \\\;count = Accum.count + 1\}$</dd>
|
||||
<dt class="fragment">Finalize(Accum)</dt>
|
||||
<dd class="fragment">$\frac{Accum.sum}{Accum.count}$</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Basic Aggregate Pattern</h3>
|
||||
<dl>
|
||||
<dt>Init</dt>
|
||||
<dd>Define a starting value for the accumulator</dd>
|
||||
<dt>Fold(Accum, New)</dt>
|
||||
<dd>Merge a new value into the accumulator</dd>
|
||||
<dt>Finalize(Accum)</dt>
|
||||
<dd>Extract the aggregate from the accumulator.</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Basic Aggregate Types</h3>
|
||||
<p class="fragment" style="font-size: 60%">Grey et. al. "Data Cube: A Relational Aggregation Operator Generalizing Group-By, Cross-Tab, and Sub-Totals</p>
|
||||
|
||||
<dl>
|
||||
<dt>Distributive</dt>
|
||||
<dd>Finite-sized accumulator and doesn't need a finalize (COUNT, SUM)</dd>
|
||||
<dt>Algebraic</dt>
|
||||
<dd>Finite-sized accumulator but needs a finalize (AVG)</dd>
|
||||
<dt>Holistic</dt>
|
||||
<dd>Unbounded accumulator (MEDIAN)</dd>
|
||||
</dl>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Group-By Aggregates</h3>
|
||||
<div style="margin-top: 60px">
|
||||
<code class="sql">SELECT SPC_COMMON, COUNT(*) FROM TREES GROUP BY SPC_COMMON</code>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Naive Idea:</b> Keep a separate accumulator for each group</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table style="font-size: 70%;">
|
||||
<tr><th>TREE_ID</th><th>SPC_COMMON</th><th>BORONAME</th><th>TREE_DBH</th></tr>
|
||||
<tr class="fragment" data-fragment-index="1"><td colspan="4">{}</td></tr>
|
||||
<tr class="fragment" data-fragment-index="2" style="font-size: smaller;"><td>180683</td><td>'red maple'</td><td>'Queens'</td><td>3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="3"><td colspan="4">{ 'red maple' = 1 }</td></tr>
|
||||
<tr class="fragment" data-fragment-index="4" style="font-size: smaller;"><td>204337</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>10</td></tr>
|
||||
<tr class="fragment" data-fragment-index="5"><td colspan="4">{ 'red maple' = 1, 'honeylocust' = 1 }</td></tr>
|
||||
<tr class="fragment" data-fragment-index="6" style="font-size: smaller;"><td>315986</td><td>'pin oak'</td><td>'Queens'</td><td>21</td></tr>
|
||||
<tr class="fragment" data-fragment-index="7"><td colspan="4">{ 'red maple' = 1, 'honeylocust' = 1, 'pin oak' = 1 }</td></tr>
|
||||
<tr class="fragment" data-fragment-index="8" style="font-size: smaller;"><td>204026</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>3</td></tr>
|
||||
<tr class="fragment" data-fragment-index="9"><td colspan="4">{ 'red maple' = 1, 'honeylocust' = 2, 'pin oak' = 1 }</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>What could go wrong?</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Alternative Grouping Algorithms</h3>
|
||||
|
||||
<dl>
|
||||
<dt>2-pass Hash Aggregate</dt>
|
||||
<dd>Like 2-pass Hash Join: Distribute groups across buckets, then do an in-memory aggregate for each bucket.</dd>
|
||||
|
||||
<dt>Sort-Aggregate</dt>
|
||||
<dd>Like Sort-Merge Join: Sort data by groups, then group elements will be adjacent.</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<svg data-src="graphics/2019-02-13-2PassHashAgg.svg" />
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table style="font-size: 70%;">
|
||||
<tr><th>TREE_ID</th><th>SPC_COMMON</th><th>BORONAME</th><th>TREE_DBH</th></tr>
|
||||
<tr class="fragment"><td colspan="4">{}</td></tr>
|
||||
<tr class="fragment" style="font-size: smaller;"><td>204337</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>10</td></tr>
|
||||
<tr class="fragment"><td colspan="4">{ 'honeylocust' = 1 }</td></tr>
|
||||
<tr class="fragment" style="font-size: smaller;"><td>204026</td><td>'honeylocust'</td><td>'Brooklyn'</td><td>3</td></tr>
|
||||
<tr class="fragment"><td colspan="4">{ 'honeylocust' = 2 }</td></tr>
|
||||
<tr class="fragment"><td colspan="4" style="font-weight: bold">... and more</td></tr>
|
||||
<tr class="fragment" style="font-size: smaller;"><td>315986</td><td>'pin oak'</td><td>'Queens'</td><td>21</td></tr>
|
||||
<tr class="fragment"><td colspan="4">{ <span class="fragment highlight-grey">'honeylocust' = 3206,</span> 'pin oak' = 1 }</td></tr>
|
||||
<tr class="fragment"><td colspan="4" style="font-weight: bold">... and more</td></tr>
|
||||
<tr class="fragment" style="font-size: smaller;"><td>180683</td><td>'red maple'</td><td>'Queens'</td><td>3</td></tr>
|
||||
<tr class="fragment"><td colspan="4">{ <span class="fragment highlight-grey">'pin oak' = 53814,</span> 'red maple' = 1 }</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<dl>
|
||||
<dt>Set/Bag Operations</dt>
|
||||
<dd>Select ($\sigma$), Project ($\pi$), Join ($\bowtie$), Union ($\cup$)</dd>
|
||||
|
||||
<dt>Bag Operations</dt>
|
||||
<dd>Distinct ($\delta$), Outer Joins (⟗)</dd>
|
||||
|
||||
<dt>List Operations</dt>
|
||||
<dd>Sort ($\tau$), Limit (L)</dd>
|
||||
|
||||
<dt>Arithmetic Operations</dt>
|
||||
<dd>Extended Projection ($\pi$), Aggregation ($\sigma$), Grouping ($\gamma$)</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
|
|
|||
|
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After Width: | Height: | Size: 15 KiB |
Loading…
Reference in a new issue