Finishing CBO slides

slides/cse4562sp2018/2018-03-05-CostBasedOptimization2.html

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       </section>
 
+      <section>
+        <section>
+          <h3>(Some) Estimation Techniques</h3>
+
+          <dl style="font-size: 80%">
+            <dt style="color: grey;">Guess Randomly</dt>
+            <dd style="color: grey;">Rules of thumb if you have no other options...</dd>
+
+            <dt style="color: grey;">Uniform Prior</dt>
+            <dd style="color: grey;">Use basic statistics to make a very rough guess.</dd>
+
+            <dt style="color: grey;">Sampling / History</dt>
+            <dd style="color: grey;">Small, Quick Sampling Runs (or prior executions of the query).</dd>
+
+            <dt style="color: grey;">Histograms</dt>
+            <dd style="color: grey;">Using more detailed statistics for improved guesses.</dd>
+
+            <dt style="color: blue;">Constraints</dt>
+            <dd style="color: blue;">Using rules about the data for improved guesses.</dd>
+          </dl>
+        </section>
+
+        <section>
+          <h3>Key / Unique Constraints</h3>
+          <pre style="margin-top: 50px;"><code class="sql">
+            CREATE TABLE R ( 
+              A int,
+              B int UNIQUE
+              ... 
+              PRIMARY KEY A
+            );
+          </code></pre>
+          <p style="margin-top: 50px;">
+            No duplicate values in the column.
+            $$\texttt{COUNT(DISTINCT A)} = \texttt{COUNT(*)}$$
+          </p>
+        </section>
+
+        <section>
+          <h3>Foreign Key Constraints</h3>
+          <pre style="margin-top: 50px;"><code class="sql">
+            CREATE TABLE S ( 
+              B int,
+              ... 
+              FOREIGN KEY B REFERENCES R.B
+            );
+          </code></pre>
+          <p style="margin-top: 50px;">
+            All values in the column appear in another table.
+            $$\pi_{attrs(S)}\left(S \bowtie_B R\right) \subseteq S$$
+          </p>
+        </section>
+
+        <section>
+          <h3>Functional Dependencies</h3>
+
+          <pre style="margin-top: 50px;"><code class="sql">
+            Not expressible in SQL
+          </code></pre>
+
+          <p style="margin-top: 50px;">
+            One set of columns uniquely determines another.<br/>
+            $\pi_{A}(\delta(\pi_{A, B}(R)))$ has no duplicates and...
+            $$\pi_{attrs(R)-A}(R) \bowtie_A \delta(\pi_{A, B}(R)) = R$$
+          </p>
+        </section>
+
+        <section>
+          <h3>Constraints</h3>
+
+          <h4>The Good</h4>
+          <ul>
+            <li style="font-size: 70%" class="fragment">Sanity check on your data: Inconsistent data triggers failures.</li>
+            <li style="font-size: 70%" class="fragment">More opportunities for query optimization.</li>
+          </ul>
+
+          <h4 style="margin-top: 50px;" class="fragment">The Not-So Good</h4>
+          <ul>
+            <li style="font-size: 70%" class="fragment">Validating constraints whenever data changes is (usually) expensive.</li>
+            <li style="font-size: 70%" class="fragment">Inconsistent data triggers failures.</li>
+          </ul>
+
+        </section>
+
+        <section>
+          <h3>Foreign Key Constraints</h3>
+
+          <p style="margin-top: 50px;">Foreign keys are like pointers.  What happens with broken pointers?</p>
+        </section>
+
+        <section>
+          <h3>Foreign Key Enforcement</h3>
+
+          <p>Foreign keys are defined with update triggers <code>ON INSERT [X]</code>, <code>ON UPDATE [X]</code>, <code>ON DELETE [X]</code>.  Depending on what [X] is, the constraint is enforced differently:</p>
+
+          <dl style="font-size: 80%">
+            <dt><code>CASCADE</code></dt>
+            <dd>Create/delete rows as needed to avoid invalid foreign keys.</dd>
+
+            <dt><code>NO ACTION</code></dt>
+            <dd>Abort any transaction that ends with an invalid foreign key reference.</dd>
+
+            <dt><code>SET NULL</code></dt>
+            <dd>Automatically replace any invalid foreign key references with NULL</dd>.
+          </dl>
+        </section>
+
+        <section>
+          <p style="font-weight: bold;">
+            <code>CASCADE</code> and <code>NO ACTION</code> ensure that the data never has broken pointers, so
+          </p>
+          $$\pi_{attrs(S)}\left(S \bowtie_B R\right) = S$$
+        </section>
+
+        <section>
+          <h3>Functional Dependencies</h3>
+
+          <p style="margin-top: 50px;"><b>A generalization of keys:</b> One set of attributes that uniquely identify another.</p>
+
+          <ul>
+            <li>SS# uniquely identifies Name.</li>
+            <li>Employee uniquely identifies Manager.</li>
+            <li>Order number uniquely identifies Customer Address.</li>
+          </ul>
+
+          <p class="fragment">Two rows with the same As must have the same Bs</p>
+          <p class="fragment" style="font-size: 80%">(but can still have identical Bs for two different As)</p>
+        </section>
+
+        <section>
+          <h3>Normal Forms</h3>
+          <p style="margin-top: 50px;">"All functional dependencies should be keys."</p>
+          <p class="fragment">(Otherwise you want two separate relations)</p>
+          <p class="fragment">(for more details, see CSE 560)</p>
+        </section>
+        
+        <section>
+          
+          $$P(A = B) = min\left(\frac{1}{\texttt{COUNT}(\texttt{DISTINCT } A)}, \frac{1}{\texttt{COUNT}(\texttt{DISTINCT } B)}\right)$$
+
+        </section>
+        <section>
+
+          <p>
+            $$R \bowtie_{R.A = S.B} S = \sigma_{R.A = S.B}(R \times S)$$
+            (and $S.B$ is a foreign key referencing $R.A$)
+          </p>
+
+          <p class="fragment" style="margin-top: 30px; font-size: 80%">
+            The (foreign) key constraint gives us two things...
+            $$\texttt{COUNT}(\texttt{DISTINCT } A) \approx \texttt{COUNT}(\texttt{DISTINCT } B)$$
+            <span style="font-size: 60%; font-weight: bold; margin: 0px;">and</span>
+            $$\texttt{COUNT}(\texttt{DISTINCT } A) = |R|$$
+          </p>
+
+          <p class="fragment" style="margin-top: 30px; font-size: 80%">
+            Based on the first property the total number of rows is roughly...
+            $$|R| \times |S| \times \frac{1}{\texttt{COUNT}(\texttt{DISTINCT } A)}$$
+          </p>
+
+          <p class="fragment" style="margin-top: 30px; font-size: 80%">
+            Then based on the second property...
+            $$ = |R| \times |S| \times \frac{1}{|R|} = |S|$$
+          </p>
+
+          <p class="fragment" style="margin-top: 30px; font-size: 50%">(Statistics/Histograms will give you the same outcome... but constraints can be easier to propagate)</p>
+        </section>
+      </section>
+
+      <section>
+        <p><b>Next class:</b> Exam Review</p>
+      </section>
+
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