Review slides
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slides: slide/2021-04-29-Provenance.html
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- date: "May 4"
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topic: "Review"
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materials:
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slides: slide/2021-05-04-Review1.html
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- date: "May 6"
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topic: "Review"
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materials:
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slides: slide/2021-05-06-Review2.html
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- date: "May 13"
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topic: "<b>Final Exam</b>"
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materials:
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src/teaching/cse-562/2021sp/slide/2021-05-04-Review1.erb
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src/teaching/cse-562/2021sp/slide/2021-05-04-Review1.erb
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---
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template: templates/cse4562_2021_slides.erb
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title: Exam Review
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date: May 4, 2021
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dependencies:
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- lib/slide_utils.rb
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---
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<%
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require "slide_utils.rb"
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%>
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<section>
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<section>
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<h3>Exam Format</h3>
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<p>You will need:<ul>
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<li>A smartphone or second device with a camera and zoom installed.</li>
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<li>A quiet, well lit area.</li>
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<li>A view of your work surface, you, and your computer screen.</li>
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</ul></p>
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</section>
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<section>
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<h3>Day-Of</h3>
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<ul>
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<li>Remember to enable "Do-not-Disturb" mode on your devices.</li>
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<li>Log into Zoom 10-15 min prior to start.</li>
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<li>Everyone logged into Zoom will be given a pin to access their exam.</li>
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<li>Write your answers on paper in dark, visible ink.</li>
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<li>Scan your exam via zoom session in a breakout room.</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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<pre><code class="sql">
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SELECT [DISTINCT] targetlist
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FROM relationlist
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WHERE condition
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</code></pre>
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<ol>
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<li class="fragment">Compute the $2^n$ combinations of tuples in all relations appearing in <span style="color: red;">relationlist</span></li>
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<li class="fragment">Discard tuples that fail the <span style="color: red;">condition</span></li>
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<li class="fragment">Delete attributes not in <span style="color: red;">targetlist</span></li>
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<li class="fragment">If <span style="font-family: Courier, fixedwidth;">DISTINCT</span> is specified, eliminate duplicate rows</li>
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</ol>
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<p style="font-size: 70%;" class="fragment">
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This is the least efficient strategy to compute a query!
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A good optimizer will find <b>more efficient strategies</b> to compute <b>the same answer.</b>
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</p>
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</section>
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<section>
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<section>
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<h2>Record Layouts</h2>
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</section>
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<section>
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<h3>Record Layout 1: Fixed</h3>
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<svg data-src="2021-05-04/record-fixed.svg" />
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</section>
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<section>
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<h3>Record Layout 2: Delimiters</h3>
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<svg data-src="2021-05-04/record-separator.svg" />
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</section>
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<section>
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<h3>Record Layout 2: Headers</h3>
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<svg data-src="2021-05-04/record-header.svg" />
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</section>
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<section>
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<dl>
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<dt>File</dt>
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<dd>A collection of pages (or records)</dd>
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<dt>Page</dt>
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<dd>A fixed-size collection of records</dd>
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<dd style="font-size: smaller;">Page size is usually dictated by hardware.<br/>Mem Page $\approx$ 4K</dd>
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td>bsp</dd>
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td>bsp</dd>
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td>nsp;Cache Line $\approx$ 64B</dd>
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<dt>Record</dt>
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<dd>One or more fields (for now)</dd>
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<dt>Field</dt>
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<dd>A primitive value (for now)</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>Relational Algebra</h3>
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<p>We start with a database <b>instance</b> with a fixed <b>schema</b></p>
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<p class="fragment" style="margin-top: 40px;">
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Queries are applied to Relations
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$$Q(\textbf{Trees}, \textbf{SpeciesInfo})$$
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</p>
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<p class="fragment" style="margin-top: 40px;">
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Queries are also Relations!
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$$Q_2(\textbf{SpeciesInfo}, Q_1(\textbf{Trees}))$$
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<span class="fragment" style="font-size: 50%; display: block; margin-top: 0px; margin-bottom: 10px;">(Relational Algebra is <u>Closed</u>)</span>
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</p>
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</section>
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<section>
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<h3>Relational Algebra</h3>
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<table style="font-size: 70%">
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<tr><th>Operation</th><th>Sym</th><th>Meaning</th></tr>
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<tr><td>Selection</td><td>$\sigma$</td><td>Select a subset of the input rows</td></tr>
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<tr><td>Projection</td><td>$\pi$</td><td>Delete unwanted columns</td></tr>
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<tr><td>Cross-product</td><td>$\times$</td><td>Combine two relations</td></tr>
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<tr><td>Set-difference</td><td>$-$</td><td>Tuples in Rel 1, but not Rel 2</td></tr>
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<tr><td>Union</td><td>$\cup$</td><td>Tuples either in Rel 1 or in Rel 2</td></tr>
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<tr><td>Intersection</td><td>$\cap$</td><td>Tuples in both Rel 1 and Rel 2</td></tr>
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<tr><td>Join</td><td>$\bowtie$</td><td>Pairs of tuples matching a specified condition</td></tr>
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<tr style="color: lightgrey;"><td>Division</td><td>$/$</td><td>"Inverse" of cross-product</td></tr>
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<tr><td>Sort</td> <td>$\tau_A$</td><td>Sort records by attribute(s) $A$</td></tr>
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<tr><td>Limit</td><td>$\texttt{LIMIT}_N$</td><td>Return only the first $N$ records<br/>(according to sort order if paired with sort).</td></tr>
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</table>
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</section>
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<section>
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<h3>RA Equivs</h3>
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<p style="font-size: 80%;">
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We say that $Q_1 \equiv Q_2$ if and only if<br/>
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we can guarantee that the <i>bag</i> of tuples produced by $Q_1(R, S, T, \ldots)$ <br/>
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is the same as the <i>bag</i> of tuples produced by $Q_2(R, S, T, \ldots)$ <br/>
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for any combination of valid inputs $R, S, T, \ldots$.
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</p>
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<p style="font-size: 70%;" class="fragment">
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... that satisfy any necessary properties.
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</p>
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</section>
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<section>
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<table style="font-size: 60%">
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<tr>
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<th>Rule</th><th>Notes</th>
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</tr>
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<tr>
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<td>$\sigma_{C_1\wedge C_2}(R) \equiv \sigma_{C_1}(\sigma_{C_2}(R))$</td>
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<td></td>
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</tr>
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<tr>
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<td>$\sigma_{C_1\vee C_2}(R) \equiv \sigma_{C_1}(R) \cup \sigma_{C_2}(R)$</td>
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<td>Note, this is only true for set, not bag union</td>
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</tr>
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<tr>
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<td>$\sigma_C(R \times S) \equiv R \bowtie_C S$</td>
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<td></td>
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</tr>
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<tr>
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<td>$\sigma_C(R \times S) \equiv \sigma_C(R) \times S$</td>
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<td>If $C$ references only $R$'s attributes, also works for joins</td>
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</tr>
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<tr>
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<td>$\pi_{A}(\pi_{A \cup B}(R)) \equiv \pi_{A}(R)$</td>
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<td></td>
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</tr>
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<tr>
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<td>$\sigma_C(\pi_{A}(R)) \equiv \pi_A(\sigma_C(R))$</td>
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<td>If $A$ contains all of the attributes referenced by $C$ </td>
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</tr>
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<tr>
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<td>$\pi_{A\cup B}(R\times S) \equiv \pi_A(R) \times \pi_B(S)$</td>
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<td>Where $A$ (resp., $B$) contains attributes in $R$ (resp., $S$)</td>
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</tr>
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<tr>
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<td>$R \times (S \times T) \equiv (R \times S) \times T$</td>
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<td>Also works for joins </td>
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</tr>
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<tr>
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<td>$R \times S \equiv S \times R$</td>
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<td>Also works for joins </td>
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</tr>
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<tr>
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<td>$R \cup (S \cup T) \equiv (R \cup S) \cup T$</td>
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<td>Also works for intersection and bag-union </td>
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</tr>
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<tr>
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<td>$R \cup S \equiv S \cup R$</td>
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<td>Also works for intersections and bag-union </td>
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</tr>
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<tr>
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<td>$\sigma_{C}(R \cup S) \equiv \sigma_{C}(R) \cup \sigma_{C}(S)$</td>
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<td>Also works for intersections and bag-union </td>
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</tr>
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<tr>
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<td>$\pi_{A}(R \cup S) \equiv \pi_{A}(R) \cup \pi_{A}(S)$</td>
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<td>Also works for intersections and bag-union </td>
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</tr>
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<tr>
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<td>$\sigma_{C}(\gamma_{A, AGG}(R)) \equiv \gamma_{A, AGG}(\sigma_{C}(R))$</td>
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<td>If $A$ contains all of the attributes referenced by $C$</td>
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</tr>
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</table>
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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>Algorithms</h3>
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<dl>
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<dt>"Volcano" Operators (Iterators)</dt>
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<dd>Operators "pull" tuples, one-at-a-time, from their children.</dd>
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<dt>2-Pass (External) Sort</dt>
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<dd>Create sorted runs, then repeatedly merge runs</dd>
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<dt>Join Algorithms</dt>
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<dd>Quickly picking out <i>specific</i> pairs of tuples.</dd>
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<dt>Aggregation Algorithms</dt>
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<dd>In-Memory vs 2-Pass, Normal vs Group-By</dd>
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</dl>
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</section>
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<section>
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<h3>Nested-Loop Join</h3>
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<svg data-src="2021-05-04/Join-NLJ.svg" />
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</section>
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<section>
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<h3>Block-Nested Loop Join</h3>
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<svg data-src="2021-05-04/Join-BNLJ.svg" class="stretch" />
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</section>
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<section>
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<h3>Strategies for Implementing $R \bowtie_{R.A = S.A} S$</h3>
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<dl>
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<dt>Sort/Merge Join</dt>
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<dd>Sort all of the data upfront, then scan over both sides.</dd>
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<dt>In-Memory Index Join (1-pass Hash; Hash Join)</dt>
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<dd>Build an in-memory index on one table, scan the other.</dd>
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<dt>Partition Join (2-pass Hash; External Hash Join)</dt>
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<dd>Partition both sides so that tuples don't join across partitions.</dd>
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</dl>
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</section>
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<section>
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<h3>Sort/Merge Join</h3>
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<svg data-src="2021-05-04/Join-SortMerge.svg" />
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</section>
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<section>
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<h3>Sort/Merge Join</h3>
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<img src="2021-05-04/Join-SortMerge.svg" />
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<p>Sort/Merge typically expressed as 3 operators<br/>(2xSort + Merge)</p>
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</section>
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<section>
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<h3>1-Pass Hash Join</h3>
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<svg data-src="2021-05-04/Join-1PassHash.svg" />
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</section>
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<section>
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<h3>2-Pass Hash Join</h3>
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<dl>
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<dt>Limited Queries</dt>
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<dd>Only supports join conditions of the form $R.A = S.B$</dd>
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<dt>Low Memory</dt>
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<dd>Never need more than 1 pair of partitions in memory</dd>
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<dt>High IO Cost</dt>
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<dd>Every record gets written out to disk, and back in.</dd>
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</dl>
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<p class="fragment">Can partition on data-values to support other types of queries.</p>
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</section>
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<section>
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<h3>Index Nested Loop Join</h3>
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To compute $R \bowtie_{R.A < S.B} S$ with an index on $S.B$
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<ol>
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<li>Read One Row of $R$</li>
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<li>Get the value of $R.A$</li>
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<li>Start index scan on $S.B > [R.A]$</li>
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<li>Return rows as normal</li>
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</ol>
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</section>
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<section>
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<h3>Basic Aggregate Pattern</h3>
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<dl>
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<dt>Init</dt>
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<dd>Define a starting value for the accumulator</dd>
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<dt>Fold(Accum, New)</dt>
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<dd>Merge a new value into the accumulator</dd>
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<dt>Finalize(Accum)</dt>
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<dd>Extract the aggregate from the accumulator.</dd>
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</dl>
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</section>
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<section>
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<h3>Basic Aggregate Types</h3>
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<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>
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<dl>
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<dt>Distributive</dt>
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<dd>Finite-sized accumulator and doesn't need a finalize (COUNT, SUM)</dd>
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<dt>Algebraic</dt>
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<dd>Finite-sized accumulator but needs a finalize (AVG)</dd>
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<dt>Holistic</dt>
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<dd>Unbounded accumulator (MEDIAN)</dd>
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</dl>
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</section>
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<section>
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<h3>Grouping Algorithms</h3>
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<dl>
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<dt>2-pass Hash Aggregate</dt>
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<dd>Like 2-pass Hash Join: Distribute groups across buckets, then do an in-memory aggregate for each bucket.</dd>
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<dt>Sort-Aggregate</dt>
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<dd>Like Sort-Merge Join: Sort data by groups, then group elements will be adjacent.</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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<p>Cost-Based Optimization</p>
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</section>
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<section>
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<h3>Accounting</h3>
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<p style="margin-top: 50px;">Figure out the cost of each <b>individual</b> operator.</p>
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<p style="margin-top: 50px;">Only count the number of IOs <b>added</b> by each operator.</p>
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</section>
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<section>
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<table style="font-size: 70%">
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<tr><th>Operation</th><th>RA</th><th>Total IOs (#pages)</th><th>Memory (#tuples)</th></tr>
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<tr >
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<td>Table Scan</td>
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<td>$R$</td>
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<td >$\frac{|R|}{\mathcal P}$</td>
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<td >$O(1)$</td>
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</tr>
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<tr >
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<td>Projection</td>
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<td>$\pi(R)$</td>
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<td >$\textbf{io}(R)$</td>
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<td >$O(1)$</td>
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</tr>
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<tr >
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<td>Selection</td>
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<td>$\sigma(R)$</td>
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<td>$\textbf{io}(R)$</td>
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<td>$O(1)$</td>
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</tr>
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<tr >
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<td>Union</td>
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<td>$R \uplus S$</td>
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<td>$\textbf{io}(R) + \textbf{io}(S)$</td>
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<td>$O(1)$</td>
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</tr>
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<tr >
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<td style="vertical-align: middle;">Sort <span >(In-Mem)</span></td>
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<td style="vertical-align: middle;">$\tau(R)$</td>
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<td >$\textbf{io}(R)$</td>
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<td >$O(|R|)$</td>
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</tr>
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<tr>
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<td >Sort (On-Disk)</td>
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<td >$\tau(R)$</td>
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<td >$\frac{2 \cdot \lfloor log_{\mathcal B}(|R|) \rfloor}{\mathcal P} + \textbf{io}(R)$</td>
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<td >$O(\mathcal B)$</td>
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</tr>
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<tr >
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<td><span >(B+Tree)</span> Index Scan</td>
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<td>$Index(R, c)$</td>
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<td >$\log_{\mathcal I}(|R|) + \frac{|\sigma_c(R)|}{\mathcal P}$</td>
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<td >$O(1)$</td>
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</tr>
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<tr>
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<td span >(Hash) Index Scan</td>
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<td span >$Index(R, c)$</td>
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<td >$1$</td>
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<td >$O(1)$</td>
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</tr>
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</table>
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<ol style="font-size: 50%; margin-top: 50px;">
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<li >Tuples per Page ($\mathcal P$) <span>– Normally defined per-schema</span></li>
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<li >Size of $R$ ($|R|$)</li>
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<li >Pages of Buffer ($\mathcal B$)</li>
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<li >Keys per Index Page ($\mathcal I$)</li>
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</ol>
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</section>
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<section>
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<table style="font-size: 70%">
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<tr><th width="300px">Operation</th><th>RA</th><th>Total IOs (#pages)</th><th style="font-size: 80%;">Mem (#tuples)</th></tr>
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<tr >
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<td style="font-size: 60%">Nested Loop Join <span >(Buffer $S$ in mem)</span></td>
|
||||
<td>$R \times_{mem} S$</td>
|
||||
<td >$\textbf{io}(R)+\textbf{io}(S)$</td>
|
||||
<td >$O(|S|)$</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="font-size: 60%">Block NLJ (Buffer $S$ on disk)</td>
|
||||
<td >$R \times_{disk} S$</td>
|
||||
<td >$\frac{|R|}{\mathcal B} \cdot \frac{|S|}{\mathcal P} + \textbf{io}(R) + \textbf{io}(S)$</td>
|
||||
<td >$O(1)$</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="font-size: 60%">Block NLJ (Recompute $S$)</td>
|
||||
<td >$R \times_{redo} S$</td>
|
||||
<td >$\textbf{io}(R) + \frac{|R|}{\mathcal B} \cdot \textbf{io}(S)$</td>
|
||||
<td >$O(1)$</td>
|
||||
</tr>
|
||||
<tr >
|
||||
<td>1-Pass Hash Join</td>
|
||||
<td>$R \bowtie_{1PH, c} S$</td>
|
||||
<td >$\textbf{io}(R) + \textbf{io}(S)$</td>
|
||||
<td >$O(|S|)$</td>
|
||||
</tr>
|
||||
<tr >
|
||||
<td>2-Pass Hash Join</td>
|
||||
<td>$R \bowtie_{2PH, c} S$</td>
|
||||
<td >$\frac{2|R| + 2|S|}{\mathcal P} + \textbf{io}(R) + \textbf{io}(S)$</td>
|
||||
<td >$O(1)$</td>
|
||||
</tr>
|
||||
<tr >
|
||||
<td>Sort-Merge Join </td>
|
||||
<td>$R \bowtie_{SM, c} S$</td>
|
||||
<td >[Sort]</td>
|
||||
<td >[Sort]</td>
|
||||
</tr>
|
||||
<tr >
|
||||
<td><span >(Tree)</span> Index NLJ</td>
|
||||
<td>$R \bowtie_{INL, c}$</td>
|
||||
<td >$|R| \cdot (\log_{\mathcal I}(|S|) + \frac{|\sigma_c(S)|}{\mathcal P})$</td>
|
||||
<td >$O(1)$</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td >(Hash) Index NLJ</td>
|
||||
<td >$R \bowtie_{INL, c}$</td>
|
||||
<td >$|R| \cdot 1$</td>
|
||||
<td >$O(1)$</td>
|
||||
</tr>
|
||||
<tr >
|
||||
<td><span >(In-Mem)</span> Aggregate</td>
|
||||
<td>$\gamma_A(R)$</td>
|
||||
<td >$\textbf{io}(R)$</td>
|
||||
<td >$adom(A)$</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="font-size: 90%">(Sort/Merge) Aggregate</td>
|
||||
<td >$\gamma_A(R)$</td>
|
||||
<td >[Sort]</td>
|
||||
<td >[Sort]</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<ol style="font-size: 50%;">
|
||||
<li>Tuples per Page ($\mathcal P$) <span>– Normally defined per-schema</span></li>
|
||||
<li>Size of $R$ ($|R|$)</li>
|
||||
<li>Pages of Buffer ($\mathcal B$)</li>
|
||||
<li>Keys per Index Page ($\mathcal I$)</li>
|
||||
<li>Number of distinct values of $A$ ($adom(A)$)</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Estimating IOs requires Estimating $|Q(R)|$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table style="font-size: 70%">
|
||||
<tr>
|
||||
<th>Operator</th>
|
||||
<th>RA</th>
|
||||
<th>Estimated Size</th>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Table</td>
|
||||
<td>$R$</td>
|
||||
<td>$|R|$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Projection</td>
|
||||
<td>$\pi(Q)$</td>
|
||||
<td>$|Q|$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Union</td>
|
||||
<td>$Q_1 \uplus Q_2$</td>
|
||||
<td>$|Q_1| + |Q_2|$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Cross Product</td>
|
||||
<td>$Q_1 \times Q_2$</td>
|
||||
<td>$|Q_1| \times |Q_2|$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Sort</td>
|
||||
<td>$\tau(Q)$</td>
|
||||
<td>$|Q|$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Limit</td>
|
||||
<td>$\texttt{LIMIT}_N(Q)$</td>
|
||||
<td>$N$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Selection</td>
|
||||
<td>$\sigma_c(Q)$</td>
|
||||
<td>$|Q| \times \texttt{SEL}(c, Q)$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Join</td>
|
||||
<td>$Q_1 \bowtie_c Q_2$</td>
|
||||
<td>$|Q_1| \times |Q_2| \times \texttt{SEL}(c, Q_1\times Q_2)$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Distinct</td>
|
||||
<td>$\delta_A(Q)$</td>
|
||||
<td>$\texttt{UNIQ}(A, Q)$</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Aggregate</td>
|
||||
<td>$\gamma_{A, B \leftarrow \Sigma}(Q)$</td>
|
||||
<td>$\texttt{UNIQ}(A, Q)$</td>
|
||||
</tr>
|
||||
</table>
|
||||
|
||||
<ul style="font-size: 50%; margin-top: 20px">
|
||||
<li>$\texttt{SEL}(c, Q)$: Selectivity of $c$ on $Q$, or $\frac{|\sigma_c(Q)|}{|Q|}$</li>
|
||||
<li>$\texttt{UNIQ}(A, Q)$: # of distinct values of $A$ in $Q$.</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>(Some) Estimation Techniques</h3>
|
||||
|
||||
<dl style="font-size: 80%">
|
||||
<div class="fragment">
|
||||
<dt>Guess Randomly</dt>
|
||||
<dd>Rules of thumb if you have no other options...</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Uniform Prior</dt>
|
||||
<dd>Use basic statistics to make a very rough guess.</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Sampling / History</dt>
|
||||
<dd>Small, Quick Sampling Runs (or prior executions of the query).</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Histograms</dt>
|
||||
<dd>Using more detailed statistics for improved guesses.</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Constraints</dt>
|
||||
<dd>Using rules about the data for improved guesses.</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Sketching</h3>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><th>Flips</th><th>Score</th><th>Probability</th>
|
||||
<th data-fragment-index="1">E[# Games]</th>
|
||||
</tr>
|
||||
<tr><td>(👽)</td><td>0</td><td>0.5</td>
|
||||
<td data-fragment-index="1">2</td>
|
||||
</tr>
|
||||
<tr><td>(🐕)(👽)</td><td>1</td><td>0.25</td>
|
||||
<td data-fragment-index="1">4</td>
|
||||
</tr>
|
||||
<tr><td>(🐕)(🐕)(👽)</td><td>2</td><td>0.125</td>
|
||||
<td data-fragment-index="1">8</td>
|
||||
</tr>
|
||||
<tr><td>(🐕)$\times N$ (👽)</td><td>$N$</td><td>$\frac{1}{2^{N+1}}$</td>
|
||||
<td>$2^{N+1}$</td>
|
||||
</tr>
|
||||
</table>
|
||||
<p style="margin-top: 50px;">If I told you that in a series of games, my best score was $N$, you might expect that I played $2^{N+1}$ games.</p>
|
||||
<p style="margin-top: 50px;">To do that, I only need to track my top score!</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Flajolet-Martin Sketches</h3>
|
||||
<h4>($\approx$ HyperLogLog)</h4>
|
||||
|
||||
<ol>
|
||||
<li>For each record...
|
||||
<ol>
|
||||
<li>Hash each record</li>
|
||||
<li>Find the index of the lowest-order non-zero bit</li>
|
||||
<li>Add the index of the bit to a set</li>
|
||||
</ol></li>
|
||||
<li>Find $R$, the lowest index <b>not</b> in the set</li>
|
||||
<li>Estimate Count-Distinct as $\frac{2^R}{\phi}$ ($\phi \approx 0.77351$)</li>
|
||||
<li>Repeat (in parallel) as needed</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Count Sketches</h3>
|
||||
|
||||
<ol>
|
||||
<li>Pick a number of "trials" and a number of "bins"</li>
|
||||
<li>For each record $O_i$
|
||||
<ol>
|
||||
<li>For each "trial" $j$
|
||||
<ol>
|
||||
<li>Use a hash function $h_j(O_i)$ to pick a bin</li>
|
||||
<li>Add a $\pm 1$ value determined by hash function $\delta_j(O_i)$ to the bin</li>
|
||||
</ol>
|
||||
</li>
|
||||
</ol>
|
||||
</ol></li>
|
||||
<li>For each trial $j$, estimate the count of $O_i$ by the value of bin $h_j(O_i)$</li>
|
||||
<li>Take the <em>median</em> value for all trials.</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Count-Min Sketches</h3>
|
||||
|
||||
<ol>
|
||||
<li>Pick a number of "trials" and a number of "bins"</li>
|
||||
<li>For each record $O_i$
|
||||
<ol>
|
||||
<li>For each "trial" $j$
|
||||
<ol>
|
||||
<li>Use a hash function $h_j(O_i)$ to pick a bin</li>
|
||||
<li>Add 1 to the bin</li>
|
||||
</ol>
|
||||
</li>
|
||||
</ol>
|
||||
</ol></li>
|
||||
<li>For each trial $j$, estimate the count of $O_i$ by the value of bin $h_j(O_i)$</li>
|
||||
<li>Take the <em>minimum</em> value for all trials.</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<dl>
|
||||
<dt>Flajolet-Martin Sketches (HyperLogLog)</dt>
|
||||
<dd>Estimating Count-Distinct</dd>
|
||||
|
||||
<dt>Count Sketches</dt>
|
||||
<dd>Estimating Count-GroupBy<br/>(roughly uniform counts)</dd>
|
||||
|
||||
<dt>Count-Min Sketches</dt>
|
||||
<dd>Estimating Count-GroupBy<br/>(small number of heavy hitters)</dd>
|
||||
</dl>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<div style="font-size: 100%;">
|
||||
$$\texttt{WHEN } \mathcal D \leftarrow \mathcal{D}+\Delta\mathcal D \texttt{ DO:}~~~~\\
|
||||
\texttt{VIEW} \leftarrow \texttt{VIEW} + \Delta Q(\mathcal D,\Delta\mathcal D)$$
|
||||
</div>
|
||||
<table style="margin-top: 50px;">
|
||||
<tr class="fragment">
|
||||
<td style="font-size: 100%;">$\Delta Q$</td>
|
||||
<td>(ideally) Small & fast query</td>
|
||||
</tr>
|
||||
<tr class="fragment">
|
||||
<td style="font-size: 100%;">$+$</td>
|
||||
<td>(ideally) Fast "merge" operation</td>
|
||||
</tr>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Intuition</h3>
|
||||
<div>
|
||||
$$\mathcal{R} = \{\ \textbf{A, B, C}\ \},\ \mathcal S = \{\ \textbf{X, Y}\ \} ~~~\Delta\mathcal{R} = \{\ \textbf{D}\ \}$$
|
||||
$$Q(\mathcal R, \mathcal S) = \texttt{COUNT}(\mathcal R \times \mathcal S)$$
|
||||
</div>
|
||||
<div style="margin-top: 50px;">
|
||||
<div class="fragment">$$ \texttt{COUNT}(\textbf{AX, AY, BX, BY, CX, CY, }\underline{\textbf{DX, DY}}) $$</div>
|
||||
<div class="fragment">$$Q(\mathcal R+\Delta\mathcal R, \mathcal S) \sim O( (|\mathcal R| + |\Delta\mathcal D|) \cdot |\mathcal S|)$$</div>
|
||||
</div>
|
||||
<div style="margin-top: 50px;">
|
||||
<div class="fragment">$$ 6 + \texttt{COUNT}(\underline{\textbf{DX, DY}}) $$</div>
|
||||
<div class="fragment">$$\texttt{VIEW} + \texttt{COUNT}(\Delta\mathcal R \times \mathcal S) \sim O(|\Delta\mathcal R| \cdot |\mathcal S|)$$</div>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$\sigma(\mathcal R) \rightarrow \sigma(\mathcal R \uplus \Delta \mathcal R)$</p>
|
||||
<p class="fragment" data-fragment-index="1">
|
||||
$ \equiv $
|
||||
<span class="fragment highlight-red" data-fragment-index="2">$\sigma(\mathcal R)$</span>
|
||||
$ \uplus $
|
||||
<span class="fragment highlight-blue" data-fragment-index="3">$\sigma(\Delta \mathcal R)$</span>
|
||||
</p>
|
||||
<div style="margin-top: 50px; font-size: 80%;">
|
||||
<p class="fragment" data-fragment-index="2" style="color: red;">$Q(\mathcal D) = \sigma(\mathcal R)$</p>
|
||||
<p class="fragment" data-fragment-index="3" style="color: #1b91ff;">$\Delta Q(\mathcal D, \Delta \mathcal D) = \sigma(\Delta \mathcal R)$</p>
|
||||
</div>
|
||||
<p class="fragment" data-fragment-index="4">Set/Bag difference also commutes through selection</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$\pi(\mathcal R) \rightarrow \pi(\mathcal R \uplus \Delta \mathcal R)$</p>
|
||||
<p class="fragment" data-fragment-index="1">
|
||||
$ \equiv $
|
||||
<span class="fragment highlight-red" data-fragment-index="2">$\pi(\mathcal R)$</span>
|
||||
$ \uplus $
|
||||
<span class="fragment highlight-blue" data-fragment-index="3">$\pi(\Delta \mathcal R)$</span>
|
||||
</p>
|
||||
<div style="margin-top: 50px; font-size: 80%;">
|
||||
<p class="fragment" data-fragment-index="2" style="color: red;">$Q(\mathcal D) = \pi(\mathcal R)$</p>
|
||||
<p class="fragment" data-fragment-index="3" style="color: #1b91ff;">$\Delta Q(\mathcal D, \Delta \mathcal D) = \pi(\Delta \mathcal R)$</p>
|
||||
</div>
|
||||
<p class="fragment" data-fragment-index="4">Does this work under set semantics?</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$\mathcal R_1 \uplus \mathcal R_2 \rightarrow \mathcal R_1 \uplus \Delta \mathcal R_1 \uplus \mathcal R_2 \uplus \Delta \mathcal R_2$</p>
|
||||
<p class="fragment" data-fragment-index="1">
|
||||
$ \equiv $
|
||||
<span class="fragment highlight-red" data-fragment-index="2">$\mathcal R_1 \uplus \mathcal R_2$</span>
|
||||
$ \uplus $
|
||||
<span class="fragment highlight-blue" data-fragment-index="3">$\Delta \mathcal R_1 \uplus \Delta \mathcal R_2$</span>
|
||||
</p>
|
||||
<div style="margin-top: 50px; font-size: 80%;">
|
||||
<p class="fragment" data-fragment-index="2" style="color: red;">$Q(\mathcal D) = \mathcal R_1 \uplus \mathcal R_2$</p>
|
||||
<p class="fragment" data-fragment-index="3" style="color: #1b91ff;">$\Delta Q(\mathcal D, \Delta \mathcal D) = \Delta \mathcal R_1 \uplus \Delta \mathcal R_2$</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<div>
|
||||
$$(\mathcal R_1 \uplus \Delta \mathcal R_1) \times (\mathcal R_2 \uplus \Delta \mathcal R_2)$$
|
||||
</div>
|
||||
<div style="margin-top: 50px;" class="fragment">
|
||||
$$\left(\mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right) \uplus \left(\Delta \mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right)$$
|
||||
</div>
|
||||
<div style="margin-top: 50px;" class="fragment">
|
||||
$$\left(\mathcal R_1 \times \mathcal R_2\right) \uplus \left(\mathcal R_1 \times \Delta \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times (\mathcal R_2 \uplus \Delta \mathcal R_2)\right)$$
|
||||
</div>
|
||||
<div style="margin-top: 50px; font-size: 90%" class="fragment">
|
||||
$$\left(\mathcal R_1 \times \mathcal R_2\right) \uplus \left(\mathcal R_1 \times \Delta \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times \mathcal R_2\right) \uplus \left(\Delta \mathcal R_1 \times \Delta \mathcal R_2\right)$$
|
||||
</div>
|
||||
</section>
|
||||
</section>
|
||||
320
src/teaching/cse-562/2021sp/slide/2021-05-04/ARIES.svg
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src/teaching/cse-562/2021sp/slide/2021-05-04/ARIES.svg
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After Width: | Height: | Size: 15 KiB |
627
src/teaching/cse-562/2021sp/slide/2021-05-06-Review2.erb
Normal file
627
src/teaching/cse-562/2021sp/slide/2021-05-06-Review2.erb
Normal file
|
|
@ -0,0 +1,627 @@
|
|||
---
|
||||
template: templates/cse4562_2021_slides.erb
|
||||
title: Exam Review
|
||||
date: May 6, 2021
|
||||
dependencies:
|
||||
- lib/slide_utils.rb
|
||||
---
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<dl>
|
||||
<dt>Atomicity</dt>
|
||||
<dd>My command gets executed fully, or not at all.</dd>
|
||||
<dt>Consistency</dt>
|
||||
<dd>The final state of the data is "sane".</dd>
|
||||
<dt>Isolation</dt>
|
||||
<dd>No concurrency glitches.</dd>
|
||||
<dt>Durability</dt>
|
||||
<dd>If things break, my data is still safe.</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Transactions</h3>
|
||||
<p>A "batch" of operations that should execute together</p>
|
||||
<dl>
|
||||
<dt>START/BEGIN TRANSACTION</dt>
|
||||
<dd>Start batching</dd>
|
||||
<dt>COMMIT</dt>
|
||||
<dd>Conclude the transaction and apply changes</dd>
|
||||
<dt>ABORT/ROLLBACK</dt>
|
||||
<dd>Undo all changes applied as part of the transaction</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<dl>
|
||||
<div class="fragment" data-fragment-index="1">
|
||||
<dt>Atomicity</dt>
|
||||
<dd>A transaction is either applied fully (COMMITed) or not at all (ABORTed).</dd>
|
||||
</div>
|
||||
<div class="fragment" data-fragment-index="2">
|
||||
<dt>Consistency</dt>
|
||||
<dd>Constraints are enforced on the final state of the transaction (and the transaction is ABORTed if they fail).</dd>
|
||||
</div>
|
||||
<div class="fragment" data-fragment-index="3">
|
||||
<div class="fragment highlight-blue" data-fragment-index="5">
|
||||
<dt>Isolation</dt>
|
||||
<dd>Two transactions running in parallel don't interfere with each other</dd>
|
||||
</div>
|
||||
</div>
|
||||
<div class="fragment" data-fragment-index="4">
|
||||
<dt>Durability</dt>
|
||||
<dd>Once the database returns from a COMMIT successfully, the data is safe from marmots</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h4>What does it mean for a transaction to be Isolated?</h4>
|
||||
<p style="font-size: 80%" class="fragment">Alice and Bob submit transactions at the same time!</p>
|
||||
|
||||
<dl>
|
||||
<div class="fragment">
|
||||
<dt>Option 1</dt>
|
||||
<dd class="fragment">Alice's transaction executes to completion.</dd>
|
||||
<dd class="fragment">Bob's transaction executes to completion.</dd>
|
||||
</div>
|
||||
<div class="fragment">
|
||||
<dt>Option 2</dt>
|
||||
<dd>Bob's transaction executes to completion.</dd>
|
||||
<dd>Alice's transaction executes to completion.</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<dl>
|
||||
<div class="fragment">
|
||||
<dt>Schedule</dt>
|
||||
<dd>A sequence of read and writes from one or more transactions to objects</dd>
|
||||
</div>
|
||||
<div class="fragment">
|
||||
<dt>Serial Schedule</dt>
|
||||
<dd>A schedule with <u>no</u> interleaving</dd>
|
||||
<dd class="fragment">... but with an arbitrary transaction order</dd>
|
||||
</div>
|
||||
<div class="fragment">
|
||||
<dt>Serial<u>izable</u> Schedule</dt>
|
||||
<dd>A schedule that produces the same output as a serial schedule</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Conflict Equivalence</h3>
|
||||
<p>Two schedules are <u>conflict equivalent</u> if there is a sequence of pairwise "flips" (of reads, or operations on different objects) that gets you from one schedule to the other.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Example 1</h3>
|
||||
<table>
|
||||
<tr><th>Time</th><th>T1</th><th>T2</th></tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td></td>
|
||||
<td><code>W(B)</code></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td><code>R(B)</code></td>
|
||||
<td class="fragment" data-fragment-index="1">↑</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td class="fragment" data-fragment-index="1">↓</td>
|
||||
<td><code>W(A)</code></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> ↓ </td>
|
||||
<td><code>W(A)</code></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p> </p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Example 1</h3>
|
||||
<table>
|
||||
<tr><th>Time</th><th>T1</th><th>T2</th></tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td></td>
|
||||
<td><code>W(B)</code></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td></td>
|
||||
<td><code>W(A)</code></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td><code>R(B)</code></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> ↓ </td>
|
||||
<td><code>W(A)</code></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p class="fragment">Conflict equivalent to a serial schedule!</p>
|
||||
</section>
|
||||
<section>
|
||||
<h3>Example 2</h3>
|
||||
<table>
|
||||
<tr><th>Time</th><th>T1</th><th>T2</th></tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td></td>
|
||||
<td><code>W(B)</code></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td><code>R(B)</code></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td><code>W(A)</code></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> ↓ </td>
|
||||
<td></td>
|
||||
<td><code>W(A)</code></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p class="fragment">Can't rewrite!</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Conflict Serializability</h3>
|
||||
<p>A schedule is <u>conflict serializable</u> if it is conflict equivalent to a serial schedule.</p>
|
||||
<p class="fragment">How do we determine if a schedule is conflict-serializable?</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Example 2</h3>
|
||||
<table style="float: left;">
|
||||
<tr><th>Time</th><th>T1</th><th>T2</th></tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td></td>
|
||||
<td><code>W(B)</code></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td><code>R(B)</code></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> | </td>
|
||||
<td><code>W(A)</code></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> ↓ </td>
|
||||
<td></td>
|
||||
<td><code>W(A)</code></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p class="fragment" style="font-size: 80%">T2's write to B "happens before" T1's read</p>
|
||||
<p class="fragment" style="font-size: 80%">T1's write to A "happens before" T2's write</p>
|
||||
<img src="2021-05-04/DependencyCycle.svg" height="150px" class="fragment"/>
|
||||
<p class="fragment" style="font-size: 80%">Cycle! No equivalent serial schedule!</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>An acyclic "Happens Before" or <u>Dependency Graph</u> is conflict serializable.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>2-Phase Locking</h3>
|
||||
|
||||
<p class="fragment">Create one lock for each object.</p>
|
||||
<p class="fragment">Each transaction operates in two "phases".</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<dl>
|
||||
<div class="fragment">
|
||||
<dt>Acquire Phase</dt>
|
||||
<dd>Before accessing an object, the transaction must acquire the object's lock.</dd>
|
||||
<dd class="fragment">The transaction does not release locks.</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Release Phase</dt>
|
||||
<dd>A transaction can release locks</dd>
|
||||
<dd class="fragment">A transaction can never again access an object it doesn't have a lock for.</dd>
|
||||
</div>
|
||||
</dl>
|
||||
|
||||
<p class="fragment">In practice, the release phase happens all at once at the end</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>All schedules created by 2PL are conflict-serializable</h3>
|
||||
<h3>Not all conflict-serializable schedules can be created by 2PL</h3>
|
||||
|
||||
<p class="fragment">$2PL \subset CS$</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Locking is...</h3>
|
||||
<dl>
|
||||
<dt>... expensive</dt>
|
||||
<dd>Costs are still incurred even if there are no problematic conflicts.</dd>
|
||||
<dt>... restrictive</dt>
|
||||
<dd>We don't know what the transaction will do, so we can't allow all schedules.</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Snapshot Isolation</h3>
|
||||
<dl>
|
||||
<div class="fragment">
|
||||
<dt>Phase 1: Read</dt>
|
||||
<dd>Transaction executes on a private copy of all accessed objects</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Phase 2: Validate</dt>
|
||||
<dd>Check if applying the transaction would break isolation</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Phase 3: Write</dt>
|
||||
<dd>Write the transaction's updates out to the main database</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
<section>
|
||||
<h3>Validation Phase</h3>
|
||||
|
||||
<p>Pick a serial order (e.g., the order in which transactions reach the validation phase)</p>
|
||||
|
||||
<p>Make sure the transaction's operations follow this order</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<dl>
|
||||
<dt>T1 and T2 read the same object</dt>
|
||||
<dd class="fragment">OK!</dd>
|
||||
|
||||
<dt>T1 reads an object written by T2 (read-write)</dt>
|
||||
<dd class="fragment">Ok. (T1's validation phase started before T2's)</dd>
|
||||
|
||||
<dt>T2 reads an object written by T1 (write-read)</dt>
|
||||
<dd class="fragment">Ok if T1-Write finishes before T2-Read starts.</dd>
|
||||
|
||||
<dt>T1 and T2 write the same object (write-write)</dt>
|
||||
<dd class="fragment">Ok if T1-Write finishes before T2-Write starts.</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>All schedules created by Snapshot Isolation are conflict-serializable</h3>
|
||||
<p class="fragment">... but Snapshot Isolation only checks for equivalence to ONE serial schedule. There might be a different, conflict-equivalent serial schedule.</p>
|
||||
<p class="fragment">$SI \subset CS$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Timestamp Concurrency Control</h3>
|
||||
<h4 style="font-size:80%; margin-bottom: 100px;">(Snapshot Isolation as seen "in practice")</h4>
|
||||
|
||||
<p>Each object $A$ gets a read timestamp ($RTS(A)$) and a write timestamp ($WTS(A)$)</p>
|
||||
|
||||
<p>Each transaction $\mathcal T$ gets a timestamp ($TS(\mathcal T)$).</p>
|
||||
|
||||
<p>(note that these can be <u>logical</u> timestamps like sequence numbers)</p>
|
||||
|
||||
<p class="fragment">(also note that real DBs don't use read timestamps... which creates problems)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>View Serializability</h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>View Equivalence</h3>
|
||||
<p>Two schedules are view-equivalent when you can transform one into the other by reordering any pair of operations that...</p>
|
||||
<ul>
|
||||
<li>operate on different objects</li>
|
||||
<li>OR, are both reads</li>
|
||||
<li>OR, are both writes to the same object, but ONLY IF the object is later overwritten by another write.</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>View Serializability</h3>
|
||||
|
||||
<p>A schedule is view serializable if it is view-equivalent to some serial schedule</p>
|
||||
|
||||
<p class="fragment">Timestamp concurrency control is guaranteed to produce view-serializable schedules.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>View Serializability</h3>
|
||||
<p>On the happens-before graph, throw away <b>edges</b> created by "hidden" write-write conflicts.</p>
|
||||
|
||||
<p>If the resulting graph is acyclic, the schedule is view serializable</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>By definition there are view serializable schedules that are not conflict serializable</h3>
|
||||
<p>$CS \subset VS$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$2PL, SI \subset CS \subset VS \subset S$</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>A long write...</h3>
|
||||
<p>What if the DB fails during a write.</p>
|
||||
|
||||
<div class="fragment">
|
||||
<p>IOs aren't atomic</p>
|
||||
<p>Atomicity and Durability might be violated!</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Buffer memory is limited...</h3>
|
||||
|
||||
<p>What if we need to page out some pages modified by a live transaction?</p>
|
||||
|
||||
<div class="fragment">
|
||||
<p>If the transaction aborts, the page state needs to be reverted.</p>
|
||||
<p>Atomicity might be violated</p>
|
||||
</div>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Write-Ahead Logging (WAL)</h3>
|
||||
<ol>
|
||||
<li>"Log" the transaction's actions</li>
|
||||
<li>Wait for the log to be safely on-disk</li>
|
||||
<li>Write the transaction's effects to disk</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Idea:</b> Periodically mark down the index of the earliest log entry still needed</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>WAL Recovery</h3>
|
||||
<ol>
|
||||
<li>Scan backwards through the log to find the checkpoint.</li>
|
||||
<li>Scan forward starting with the checkpointed 'first log entry' to find all transactions with a <code>COMMIT</code> entry.</li>
|
||||
<li>Replay log entries starting with the checkpointed 'first log entry', ignoring non-<code>COMMIT</code>ed transactions.</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Undo-Logging</h2>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Log</h3>
|
||||
<table>
|
||||
<tr>
|
||||
<th>Timestamp</th>
|
||||
<th>Transaction</th>
|
||||
<th>Object</th>
|
||||
<th>Value</th>
|
||||
<th class="fragment" data-fragment-index="2">Prev</th>
|
||||
</tr>
|
||||
<tr><td>10</td><td>T1</td><td>Page 5</td><td>1010...</td><td class="fragment" data-fragment-index="2">00101...</td></tr>
|
||||
<tr><td>11</td><td>T2</td><td>Page 3</td><td>1000...</td><td class="fragment" data-fragment-index="2">0111...</td></tr>
|
||||
<tr><td>12</td><td>T1</td><td>Page 1</td><td>0011...</td><td class="fragment" data-fragment-index="2">0001...</td></tr>
|
||||
<tr><td>13</td><td>T3</td><td>Page 5</td><td>1100...</td><td class="fragment" data-fragment-index="2">1010</td></tr>
|
||||
</table>
|
||||
<p class="fragment" data-fragment-index="1"><b>Idea: </b> Record the page's previous value.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Recovering after a crash</h3>
|
||||
<ol>
|
||||
<li>Rebuild in-memory state (Analyze)</li>
|
||||
<li>Rebuild buffer manager (Redo)</li>
|
||||
<li>Abort uncommitted transactions (Undo)</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>ARIES Recovery</h3>
|
||||
<svg data-src="2021-05-04/ARIES.svg" class="stretch" />
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<h3>Datalog</h3>
|
||||
<code>[head] :- [body]</code>
|
||||
<p class="fragment">$$Q(A) :-~~ R(A, B), S(B, C)$$</p>
|
||||
<p class="fragment">like <code>SELECT A FROM R NATURAL JOIN S</code></p>
|
||||
<dl class="fragment">
|
||||
<dt>A</dt>
|
||||
<dd>Head Variable (appears in the head and body)</dd>
|
||||
<dt>B, C</dt>
|
||||
<dd>Existential Variables (appear only in the body)</dd>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>Stop thinking about relations as collections of <b>records</b>, and instead think of them as collections of <b>facts</b></p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<%= data_table(["A", "B"], [[1, 2], [1, 3], [2, 3], [2, 4]], name: "R", rowids: true) %>
|
||||
<p class="fragment">The fact $R(1, 2)$ is <b>true</b>.</p>
|
||||
<p class="fragment">The fact $R(2, 1)$ is <b>false</b> (or unknown).</p>
|
||||
<p class="fragment">A table contains all facts that are provably true.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p style="margin-bottom: 50px;">$$Q(A) :-~~ R(A, B), S(B, C)$$</p>
|
||||
For any $A$, the fact $Q(A)$ is true if...
|
||||
<ul>
|
||||
<li class="fragment">there is some $B$ and $C$ for which...</li>
|
||||
<li class="fragment">the fact $R(A, B)$ is true, and...</li>
|
||||
<li class="fragment">the fact $S(B, C)$ is true.</li>
|
||||
</ul>
|
||||
<p class="fragment" style="margin-top: 50px;">$\forall A : \big( \exists B, C : R(A, B) \wedge S(B, C) \big) \rightarrow Q(A)$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p style="margin-bottom: 50px;">
|
||||
$$Q(A) :-~~ R(A, B), S(B, C)$$
|
||||
$$Q(A) :-~~ R(A, B), R(B, C)$$
|
||||
</p>
|
||||
|
||||
<p>Treat multiple rules as a disjunction. <br/>($Q(A)$ is true if <b>any</b> rule is satisfied)</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>As powerful as Set-RA</h3>
|
||||
|
||||
<dl>
|
||||
<div class="fragment">
|
||||
<dt>Projection</dt>
|
||||
<dd>$Q := \pi_A(R)$</dd>
|
||||
<dd>$Q(A) :-~~ R(A, \ldots)$</dd>
|
||||
</div>
|
||||
<div class="fragment">
|
||||
<dt>Union</dt>
|
||||
<dd>$Q := R \cup S$</dd>
|
||||
<dd>$Q(\ldots) :-~~ R(\ldots)$</dd>
|
||||
<dd>$Q(\ldots) :-~~ S(\ldots)$</dd>
|
||||
</div>
|
||||
<div class="fragment">
|
||||
<dt>Join</dt>
|
||||
<dd>$Q := R \bowtie S$</dd>
|
||||
<dd>$Q(\ldots) :-~~ R(\ldots), S(\ldots)$</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<dl>
|
||||
<dt>Selection (Equality)</dt>
|
||||
<dd>$Q := \sigma_{R.A = R.B}(R)$</dd>
|
||||
<dd>$Q(A) :-~~ R(A, A)$</dd>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Selection (Equality')</dt>
|
||||
<dd>$Q := \sigma_{R.A = 1}(R)$</dd>
|
||||
<dd>$Q(B) :-~~ R(1, B)$</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment">
|
||||
<dt>Selection (Other)</dt>
|
||||
<dd>$Q := \sigma_{A > B}(R)$</dd>
|
||||
<dd>$Q(A,B) :-~~ R(A, B), [[ A > B ]]$</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<%= data_table(
|
||||
["A", "B"],
|
||||
[[1, 0], [2, 0], [3, 0], "...", [2, 1], "..."],
|
||||
name: "$[[ A > B ]]$",
|
||||
build_in: :by_row
|
||||
)%>
|
||||
<p class="fragment">Relations are Sets of Facts. We can have a relation consisting of all pairs $A, B$ where $A$ is bigger.</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section>
|
||||
<ul>
|
||||
<li>Why is this tuple in my query result?</li>
|
||||
<li class="fragment">Why is this tuple <b>not</b> in my query result?</li>
|
||||
<li class="fragment">Which datasets were used to create this value?</li>
|
||||
<li class="fragment">How does this input affect my query output?</li>
|
||||
</ul>
|
||||
<h3 class="fragment" style="margin-top: 50px;">Provenance</h3>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>How does the input data relate to a query output.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h3>Types of Provenance</h3>
|
||||
<dl style="font-size: 80%">
|
||||
<div class="fragment" data-fragment-index="1">
|
||||
<div class="fragment highlight-blue" data-fragment-index="6">
|
||||
<dt>Why Provenance (Lineage)</dt>
|
||||
<dd>What's the smallest fragment of my input needed to produce some row</dd>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div class="fragment" data-fragment-index="2">
|
||||
<dt>Why-Not Provenance</dt>
|
||||
<dd>What's the least I can add to my input to get a desired row</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment" data-fragment-index="3">
|
||||
<div class="fragment highlight-blue" data-fragment-index="6">
|
||||
<dt>How Provenance</dt>
|
||||
<dd>An execution trace of the result; <u>How</u> were the tuples combined?</dd>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div class="fragment" data-fragment-index="4">
|
||||
<dt>Where Provenance</dt>
|
||||
<dd>Which cell(s) was a given output value taken from</dd>
|
||||
</div>
|
||||
|
||||
<div class="fragment" data-fragment-index="5">
|
||||
<dt>Taint</dt>
|
||||
<dd>Was the output affected by any "tainted" input cell/row</dd>
|
||||
</div>
|
||||
</dl>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p><b>Idea: </b> Arithmetic models how a tuple was derived pretty well.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$[[ R(a, b) ]] \rightarrow \texttt{constant}$</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$[[R(a, b) \cup S(a, b)]] \rightarrow [[R(a, b)]] \oplus [[S(a, b)]] $</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$[[R(a, b) \times S(c, d)]] \rightarrow [[R(a, b)]] \otimes [[S(c, d)]] $</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<p>$[[\pi_a R(a, b)]] \rightarrow \sum_b [[R(a, b)]]]] $</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<table>
|
||||
<tr><th>$\oplus$</th><th>$\otimes$</th><th>Effect</th></tr>
|
||||
<tr><td>$+$</td><td>$\times$</td><td>Bag multiplicity</td></tr>
|
||||
<tr><td>$\vee$</td><td>$\wedge$</td><td>Set existence</td></tr>
|
||||
<tr><td>$\cup$</td><td>$\times$</td><td>Why provenance</td></tr>
|
||||
<tr><td>min</td><td>max</td><td>Access control</td></tr>
|
||||
</table>
|
||||
</section>
|
||||
</section>
|
||||
Loading…
Reference in a new issue