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@ -27,15 +27,54 @@ textbook: Ch. 20.1, 20.3, 20.4
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</section>
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<section>
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<img src="2021-03-18/node_resources.svg" height="500px">
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<img src="2021-03-18/node_resources.svg" height="500px" />
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</section>
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<section>
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<h3>Communication Models</h3>
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<img src="2021-03-18/communication_base.svg" />
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</section>
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<section>
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<h3>Splitting Work</h3>
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<h3>Shared Memory</h3>
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<img src="2021-03-18/communication_sharedmem.svg" />
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</section>
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<section>
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<h3>Non-Uniform Memory Access</h3>
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<img src="2021-03-18/communication_numa.svg" />
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</section>
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<section>
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<h3>Shared Nothing / Message Passing</h3>
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<img src="2021-03-18/communication_sharednothing.svg" />
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</section>
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<section>
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<dl>
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<dt class="fragment highlight-grey" data-fragment-index=1>Shared Memory</dt>
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<dd class="fragment highlight-grey" data-fragment-index=1>HDFS, S3, RAM+Modern OSes</dd>
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<dt class="fragment highlight-grey" data-fragment-index=1>NUMA</dt>
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<dd class="fragment highlight-grey" data-fragment-index=1>AMD CPUs</dd>
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<dt>Shared Nothing</dt>
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<dd>MPP, Actor Model</dd>
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<p class="fragment" data-fragment-index=1>Today we want to clearly see the communications.</p>
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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>The Basic Model</h3>
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<svg data-src="2021-03-18/single_worker.svg" />
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</section>
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<section>
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<h3>Putting Workers Together</h3>
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<svg data-src="2021-03-18/assembly_line.svg" height="500px"/>
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@ -43,7 +82,39 @@ textbook: Ch. 20.1, 20.3, 20.4
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</section>
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<section>
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<svg data-src="2021-03-18/bottlenecks.svg" />
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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>No Parallelism</h3>
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<img src="2021-03-18/query.svg">
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<attribution>freesvg.org</attribution>
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</section>
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<section>
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<h3>"Pipeline" Parallelism</h3>
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<img src="2021-03-18/query_pipeline.svg">
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<attribution>freesvg.org</attribution>
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</section>
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<section>
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<h3>"Pipeline" Parallelism</h3>
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<img src="2021-03-18/query_partition.svg">
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<attribution>freesvg.org</attribution>
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</section>
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<section>
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<h3>Together</h3>
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<img src="2021-03-18/query_full.svg">
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<attribution>freesvg.org</attribution>
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</section>
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</section>
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<section>
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<section>
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<svg data-src="2021-03-18/partition_challenge.svg" />
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</section>
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<section>
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@ -51,17 +122,400 @@ textbook: Ch. 20.1, 20.3, 20.4
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<table>
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<tr>
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<th>Replication</th>
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<th class="fragment highlight-grey" data-fragment-index=3>Replication</th>
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<td style="width: 20px"></td>
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<th>Partitioning (Sharding)</th>
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</tr>
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<tr>
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<td><img class="fragment" src="2021-03-18/replication.svg" /></td>
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<td><img class="fragment" data-fragment-index=1 src="2021-03-18/replication.svg" /></td>
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<td></td>
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<td><img class="fragment" src="2021-03-18/partitioning.svg" /></td>
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<td><img class="fragment" data-fragment-index=2 src="2021-03-18/partitioning.svg" /></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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<h3>How to Partition Data?</h3>
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<ul>
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<li>Arbitrarily</li>
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<li class="fragment highlight-grey" data-fragment-index="2">Range</li>
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<li class="fragment highlight-grey" data-fragment-index="2">Hash</li>
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</ul>
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<p class="fragment" data-fragment-index="1" style="font-size: 70%">look familiar?</p>
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</section>
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<section>
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<p>Can we run each worker on one partition?</p>
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</section>
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<section>
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<h3>Filter</h3>
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<h2 class="fragment">Yes</h2>
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<p class="fragment">$N$ partitions in, $N$ partitions out</p>
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</section>
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<section>
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<h3>Project</h3>
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<h2 class="fragment">Yes</h2>
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<p class="fragment">$N$ partitions in, $N$ partitions out</p>
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</section>
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<section>
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<h3>Union</h3>
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<h2 class="fragment">Yes</h2>
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<p class="fragment">Trick question, just combines partitions!</p>
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</section>
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<section>
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<h3>(Single-row) Aggregate</h3>
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<h2 class="fragment">No</h2>
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<p class="fragment">$N$ partitions in, $1$ partition out</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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<svg data-src="2021-03-18/query_aggregate.svg" />
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</section>
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<section>
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<h3>Partial Aggregation</h3>
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<dl>
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<dt>Algebraic Aggregates (Count, Sum, Avg, Min, Max)</dt>
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<dd>Bounded-size intermediate state</dd>
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<dt class="fragment highlight-grey" data-fragment-index=1>Holistic Aggregates (Median, Mode, Count-Distinct)</dt>
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<dd class="fragment highlight-grey" data-fragment-index=1><b>Un</b>bounded-size intermediate state</dd>
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</dl>
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</section>
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<section>
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<div>
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$$\Sigma_{SUM} (R_1 \uplus R_2 \uplus \ldots \uplus R_N)$$
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</div>
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<p class="fragment">Aggregate needs to process $N$ <b>partitions</b>.</p>
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<div class="fragment" style="margin-top: 100px">
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$$\Sigma_{SUM} (\Sigma_{SUM}(R_1) \uplus \Sigma_{SUM}(R_2) \uplus \ldots \uplus \Sigma_{SUM}(R_N))$$
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</div>
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<p class="fragment">Final aggregate only needs to process $N$ <b>tuples</b>.</p>
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</section>
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<section>
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<div>
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$$\Sigma_{AVG} (R_1 \uplus R_2 \uplus \ldots \uplus R_N)$$
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</div>
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<p>↓↓↓↓↓</p>
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<div>
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$$\Sigma_{\frac{SUM(A)}{SUM(B)}} (\Sigma_{A \leftarrow SUM,\; B \leftarrow COUNT}(R_1) \ldots \Sigma_{A \leftarrow SUM,\; B \leftarrow COUNT}(R_N))$$
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</div>
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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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<dt class="fragment" data-fragment-index=1>Merge(Accum, Accum)</dt>
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<dd class="fragment" data-fragment-index=1>Merge two accumulators together.</dd>
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</dl>
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</section>
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<section>
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<img src="2021-03-18/query_aggregate_merge.svg" />
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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>Joins</h3>
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<h2 class="fragment">No</h2>
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<p class="fragment">Every partition from one table needs to pair <br/>with every partition from the other.</p>
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</section>
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<section>
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$$(R_1 \uplus \ldots \uplus R_N) \bowtie (S_1 \uplus \ldots \uplus S_K)$$
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<p style="margin-bottom: 50px; margin-top: 50px;">↓↓↓↓↓↓</p>
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$$(R_1 \bowtie S_1) \uplus \ldots \uplus (R_1 \bowtie S_K)$$
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$$\ldots\uplus \ldots \uplus \ldots$$
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$$(R_N \bowtie S_1) \uplus \ldots \uplus (R_N \bowtie S_K)$$
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</section>
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<section>
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<table>
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<tr>
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<td></td>
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<% (1..4).each do |j| %><td>$S_<%= j %>$</td><%end%>
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</tr>
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<% (1..4).each do |i| %>
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<tr>
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<td>$R_<%=i%>$</td>
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<% (1..4).each do |j| %><td>$R_<%=i%>\bowtie S_<%=j%>$</td><%end%>
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</tr>
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<% end %>
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</table>
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<p class="fragment">$N$ workers gets us $\sqrt{N}$ scaling</p>
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</section>
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<section>
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<h3>How to Partition Data?</h3>
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<ul>
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<li class="fragment highlight-current-blue" data-fragment-index=1>Arbitrarily</li>
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<li class="fragment highlight-current-blue" data-fragment-index=2>Range</li>
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<li class="fragment highlight-current-blue" data-fragment-index=2>Hash</li>
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</ul>
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</section>
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<section>
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$$R \bowtie_{A} S$$
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$$R_i = \sigma_{\texttt{hash}(A) = i}(R)$$
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$$S_i = \sigma_{\texttt{hash}(A) = i}(S)$$
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</section>
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<section>
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<table>
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<tr>
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<td></td>
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<% (1..4).each do |j| %><td>$S_<%= j %>$</td><%end%>
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</tr>
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<% (1..4).each do |i| %>
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<tr>
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<td>$R_<%=i%>$</td>
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<% (1..4).each do |j| %>
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<% if i == j %>
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<td>$R_<%=i%>\bowtie S_<%=j%>$</td>
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<% else %>
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<td class="fragment highlight-grey" data-fragment-index=1>$R_<%=i%>\bowtie S_<%=j%>$</td>
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<% end %>
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<% end %>
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</tr>
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<% end %>
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</table>
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<p class="fragment">Back to $N$ scaling for $N$ workers</p>
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</section>
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<section>
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<p>What if the partitions aren't aligned so nicely?</p>
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</section>
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<section>
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<svg data-src="2021-03-18/reshuffle.svg" />
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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>Can we do better?</p>
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<p class="fragment">Focus on $R_1 \bowtie_B S_1$</p>
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<p style="margin-top: 100px" class="fragment"><b>Problem: </b> All tuples in $R_1$ and $S_1$ need to be<br/> sent to the same worker.</p>
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</section>
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<section>
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<h3>Data Transfer</h3>
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<ul>
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<li>Limited IO/<span class="fragment highlight-blue">Network</span> bandwidth</li>
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<li>Compute needed to receive data</li>
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</ul>
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</section>
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<section>
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<p><b>Idea 1</b>: Put the worker on the node that has the data!</p>
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<p class="fragment" style="margin-top: 100px"><b>Problem:</b> What if the data is on 2 different nodes?</p>
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<p class="fragment" style="margin-top: 100px"><b>Idea 1.b:</b> Put the worker on one of the nodes with data.</p>
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</section>
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<section>
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<p>Can we reduce network use more?</p>
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</section>
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<section>
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<svg data-src="2021-03-18/semijoin_naive.svg" />
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</section>
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<section>
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<svg data-src="2021-03-18/semijoin_actual.svg" />
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</section>
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<section>
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<svg data-src="2021-03-18/semijoin_example.svg" />
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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><b>Problem: </b> Worker 2 is still sending a lot of data.</p>
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<p class="fragment" style="margin-top: 50px;"><b>Idea:</b> Compress $\pi_B(S_1)$</p>
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</section>
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<section>
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<h3>Lossy Compression</h3>
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<p>(not all errors are equal)</p>
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<dl>
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<dt class="fragment">False Positives</dt>
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<dd class="fragment">($b \in \pi_B(S_1)$ when it isn't)</dd>
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<dd class="fragment">not ideal, but ok</dd>
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<dt class="fragment">False Negatives</dt>
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<dd class="fragment">($b \not\in \pi_B(S_1)$ when it is)</dd>
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<dd class="fragment">bad, wrong answer!</dd>
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</dl>
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</section>
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<section>
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<h3>Bloom Filters</h3>
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$$filter \leftarrow \texttt{Bloom}(\textbf{Alice}, \textbf{Bob}, \textbf{Carol}, \textbf{Dave})$$
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<table style="margin-top: 100px;">
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<tr>
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<td class="fragment"><b>User</b>: Is Alice part of the set?</td>
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<td class="fragment">$filter$: Yes</td>
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</tr>
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<tr>
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<td class="fragment"><b>User</b>: Is Eve part of the set?</td>
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<td class="fragment">$filter$: No</td>
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</tr>
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<tr>
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<td class="fragment"><b>User</b>: Is Fred part of the set?</td>
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<td class="fragment">$filter$: Yes</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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<h3>Bloom Filter</h3>
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<p style="margin-top: 50px;">Test <b>always</b> returns Yes if the element is in the set.</p>
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<p style="margin-top: 50px;">Test <b>usually</b> returns No if the element is not in the set.</p>
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</section>
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<section>
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<h3>Bloom Filters</h3>
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<p style="margin-top: 50px;">A bloom filter is an array of bits.</p>
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<p style="margin-top: 50px;">$M$: Number of bits in the array.</p>
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<p style="margin-top: 50px;">$K$: Number of hash functions.</p>
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</section>
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<section>
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<h3>For one record/key</h3>
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<ol>
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<li class="fragment">$\forall i \in [M] : filter[i] = 0$</li>
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<li class="fragment">$\forall j \in [K] : filter[\texttt{hash}_j(key)] = 1$</li>
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</ol>
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<p class="fragment">Each bit vector has $\sim K$ bits set.</p>
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</section>
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<section>
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<table>
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<tr>
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<td>$Key_1$</td>
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<td>00101010</td>
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</tr>
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<tr>
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<td>$Key_2$</td>
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<td>01010110</td>
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</tr>
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<tr>
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<td>$Key_3$</td>
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<td>10000110</td>
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</tr>
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<tr>
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<td>$Key_4$</td>
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<td>01001100</td>
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</tr>
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</table>
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<div class="fragment">
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<h4 style="margin-top: 30px;">Filters are combined by Bitwise-OR</h4>
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$$Key_1 \;|\; Key_2 = 01111110$$
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</div>
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<div class="fragment">
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<h4 style="margin-top: 30px;">Test for inclusion by checking for bits</h4>
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$$Key_i \;\&\; filter = Key_i$$
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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>
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<td>$Key_1$</td>
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<td>00101010</td>
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</tr>
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<tr>
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<td>$Key_2$</td>
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<td>01010110</td>
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</tr>
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<tr>
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<td>$Key_3$</td>
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<td>10000110</td>
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</tr>
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<tr>
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<td>$Key_4$</td>
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<td>01001100</td>
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</tr>
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</table>
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<div style="margin-top: 50px">
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$$Key_1 \;|\; Key_2 = 01111110$$
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</div>
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|
||||
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<td class="fragment">$Key_1 \;\&\; 01111110$</td>
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<td class="fragment">00101010</td>
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<p class="fragment">(False positive)</p>
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<section>
|
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<b>Next time:</b> Online Aggregation/AQP
|
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</section>
|
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260
src/teaching/cse-562/2021sp/slide/2021-03-18/bottlenecks.svg
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After Width: | Height: | Size: 17 KiB |
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Reference in a new issue