363 lines
11 KiB
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363 lines
11 KiB
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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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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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