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ExtRA+Sort

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Oliver Kennedy 2018-02-13 23:22:39 -05:00
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slides/cse4562sp2018/2018-02-12-Algorithms.html
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@ -161,7 +161,7 @@
In particular, spend a bunch of time setting up the framework first. We'll need to
cover attribution of costs to individual operators (e.g., Select doesn't introduce IOs)
Also worth covering: IOs vs Record Reads
Also worth covering: IOs vs Record Reads.
-->
<h3>Select</h3>
<svg data-src="graphics/2018-02-12-Flow-Select.svg" />

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slides/cse4562sp2018/2018-02-14-ExtRA.html
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<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>
<dd>Distinct ($\delta$), Outer Joins (⟗)</dd>
<dt>List Operations</dt>
<dd>Sort ($\tau$), Limit</dd>
@ -76,9 +76,95 @@
</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><td>Unknown</td><td>AND</td><td>True</td><td>$\equiv$</td><td>Unknown</td></tr>
<tr><td>Unknown</td><td>AND</td><td>False</td><td>$\equiv$</td><td>False</td></tr>
<tr><td colspan="5"></td></tr>
<tr><td>Unknown</td><td>OR</td><td>Unknown</td><td>$\equiv$</td><td>Unknown</td></tr>
<tr><td>Unknown</td><td>OR</td><td>True</td><td>$\equiv$</td><td>True</td></tr>
<tr><td>Unknown</td><td>OR</td><td>False</td><td>$\equiv$</td><td>Unknown</td></tr>
<tr><td colspan="5"></td></tr>
<tr><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>
$$Streets \bowtie_{StreetName} Trees$$
<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>
@ -140,7 +226,7 @@
<section>
<p>What's the bottleneck?</p>
<p class="fragment">IO Cost: $O(N \cdot \log_2(N))$<br/>(with $N$ blocks)</p>
<p class="fragment">IO Cost: $O(N \cdot \lceil\log_2(N)\rceil)$<br/>(with $N$ blocks)</p>
</section>
<section>
@ -153,12 +239,57 @@
<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>
<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>
</div></div>

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