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GraphProcessingPipeline.html

GraphProcessingPipeline.html 51.46 KB

<!DOCTYPE html>
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 <title>Learning from Examples &raquo; Graph Processing Pipeline | Taskflow QuickStart</title>
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<main><article>
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 <h1>
 <a href="Examples.html">Learning from Examples</a> &raquo;
 Graph Processing Pipeline
 </h1>
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 <h3>Contents</h3>
 <ul>
 <li><a href="#FormulateTheGraphProcessingPipelineProblem">Formulate the Graph Processing Pipeline Problem</a></li>
 <li>
 <a href="#CreateAGraphProcessingPipeline">Create a Graph Processing Pipeline</a>
 <ul>
 <li><a href="#GraphPipelineFindATopologicalOrderOfTheGraph">Find a Topological Order of the Graph</a></li>
 <li><a href="#GraphPipelineDefineTheStageFunction">Define the Stage Function</a></li>
 <li><a href="#GraphPipelineDefineThePipes">Define the Pipes</a></li>
 <li><a href="#GraphPipelineDefineTheTaskGraph">Define the Task Graph</a></li>
 <li><a href="#GraphPipelineSubmitTheTaskGraph">Submit the Task Graph</a></li>
 </ul>
 </li>
 <li><a href="#GraphPipelineReference">Reference</a></li>
 </ul>
 </nav>
We study a graph processing pipeline that propagates a sequence of linearly dependent tasks over a dependency graph. In this particular workload, we will learn how to transform task graph parallelism into pipeline parallelism.<section id="FormulateTheGraphProcessingPipelineProblem"><h2><a href="#FormulateTheGraphProcessingPipelineProblem">Formulate the Graph Processing Pipeline Problem</a></h2>Given a directed acyclic graph (DAG), where each node encapsulates a sequence of linearly dependent tasks, namely stage tasks, and each edge represents a dependency between two tasks at the same stages of adjacent nodes. For example, assuming <code>fi(u)</code> represents the <code>i</code>th-stage task of node <code>u</code>, a dependency from <code>u</code> to <code>v</code> requires <code>fi(u)</code> to run before <code>fi(v)</code>. The following figures shows an example of three stage tasks in a DAG of three nodes (<code>A</code>, <code>B</code>, and <code>C</code>) and two dependencies (<code>A-&gt;B</code> and <code>A-&gt;C</code>):<div class="m-graph"><svg style="width: 18.000rem; height: 14.800rem;" viewBox="0.00 0.00 180.00 148.00">
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<title>L</title>
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<text text-anchor="start" x="55" y="-128" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">[Node A]</text>
<text text-anchor="start" x="55" y="-117" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 1: f1(A)</text>
<text text-anchor="start" x="55" y="-106" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 2: f2(A)</text>
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<text text-anchor="start" x="103" y="-29" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 1: f1(C)</text>
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</div>While we can directly create a taskflow for the DAG (i.e., each task in the taskflow runs <code>f1</code>, <code>f2</code>, and <code>f3</code> sequentially), we can describe the parallelism as a three-stage pipeline that propagates a topological order of the DAG through three stage tasks. Consider a valid topological order of this DAG, <code>A, B, C</code>, its pipeline parallelism can be illustrated in the following figure:<div class="m-graph"><svg style="width: 20.600rem; height: 33.200rem;" viewBox="0.00 0.00 206.00 332.00">
<g transform="scale(1 1) rotate(0) translate(4 328)">
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<title>f3_A&#45;&gt;f3_B</title>
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<title>f2_B&#45;&gt;f2_C</title>
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</div>At the beginning, <code>f1(A)</code> runs first. When <code>f1(A)</code> completes, it moves on to <code>f2(A)</code> and, meanwhile, <code>f1(B)</code> can start to run together with <code>f2(A)</code>, and so on so forth. The straight line represents two parallel tasks that can overlap in time in the pipeline. For example, <code>f3(A)</code>, <code>f2(B)</code>, and <code>f1(C)</code> can run simultaneously. The following figures shows the task dependency graph of this pipeline workload:<div class="m-graph"><svg style="width: 20.600rem; height: 18.800rem;" viewBox="0.00 0.00 206.00 188.00">
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<title>f1_B&#45;&gt;f2_B</title>
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<title>f1_C&#45;&gt;f2_C</title>
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<title>f2_A&#45;&gt;f3_A</title>
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<g class="m-edge">
<title>f2_B&#45;&gt;f2_C</title>
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<g class="m-edge">
<title>f2_B&#45;&gt;f3_B</title>
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<title>f3_C</title>
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<title>f2_C&#45;&gt;f3_C</title>
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<g class="m-edge">
<title>f3_A&#45;&gt;f3_B</title>
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<g class="m-edge">
<title>f3_B&#45;&gt;f3_C</title>
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</div>As we can see, tasks in diagonal lines (lower-left to upper-right) can run in parallel. This type of parallelism is also referred to as wavefront parallelism, which sweeps parallel elements in a diagonal direction.<aside class="m-note m-info"><h4>Note</h4>Depending on the graph size and the number of stage tasks, task graph parallelism and pipeline parallelism can bring very different performance results. For example, a small graph will a long chain of stage tasks may perform better with pipeline parallelism than task graph parallelism, and vice versa.</aside></section><section id="CreateAGraphProcessingPipeline"><h2><a href="#CreateAGraphProcessingPipeline">Create a Graph Processing Pipeline</a></h2>Using the example from the previous section, we create a three-stage pipeline that encapsulates the three stage tasks (<code>f1, f2, f3</code>) in three pipes. By finding a topological order of the graph, we can transform the node dependency into a sequence of linearly dependent data tokens to feed into the pipeline. The overall implementation is shown below:<pre class="m-code">#include &lt;taskflow/taskflow.hpp&gt;
#include &lt;taskflow/algorithm/pipeline.hpp&gt;

// 1st-stage function
void f1(const std::string&amp; node) {
 printf(&quot;f1(%s)\n&quot;, node.c_str());
}

// 2nd-stage function
void f2(const std::string&amp; node) {
 printf(&quot;f2(%s)\n&quot;, node.c_str());
}

int main() {

tf::Taskflow taskflow(&quot;graph processing pipeline&quot;);
 tf::Executor executor;

const size_t num_lines = 2;
 
 // a topological order of the graph
 // |-&gt; B
 // A--|
 // |-&gt; C
 const std::vector&lt;std::string&gt; nodes = {&quot;A&quot;, &quot;B&quot;, &quot;C&quot;};

// the pipeline consists of three serial pipes
 // and up to two concurrent scheduling tokens
 tf::Pipeline pl(num_lines,

// first pipe calls f1
 tf::Pipe{tf::PipeType::SERIAL, [&amp;](tf::Pipeflow&amp; pf) {
 if(pf.token() == nodes.size()) {
 pf.stop();
 }
 else {
 f1(nodes[pf.token()]);
 }
 }},
 
 // second pipe calls f2
 tf::Pipe{tf::PipeType::SERIAL, [&amp;](tf::Pipeflow&amp; pf) {
 f2(nodes[pf.token()]);
 }},

// third pipe calls f3
 tf::Pipe{tf::PipeType::SERIAL, [&amp;](tf::Pipeflow&amp; pf) {
 f3(nodes[pf.token()]);
 }}
 );

// build the pipeline graph using composition
 tf::Task init = taskflow.emplace([](){ std::cout &lt;&lt; &quot;ready\n&quot;; })
 .name(&quot;starting pipeline&quot;);
 tf::Task task = taskflow.composed_of(pl)
 .name(&quot;pipeline&quot;);
 tf::Task stop = taskflow.emplace([](){ std::cout &lt;&lt; &quot;stopped\n&quot;; })
 .name(&quot;pipeline stopped&quot;);

// create task dependency
 init.precede(task);
 task.precede(stop);

// dump the pipeline graph structure (with composition)
 taskflow.dump(std::cout);

// run the pipeline
 executor.run(taskflow).wait();

return 0;
}</pre><section id="GraphPipelineFindATopologicalOrderOfTheGraph"><h3><a href="#GraphPipelineFindATopologicalOrderOfTheGraph">Find a Topological Order of the Graph</a></h3>The first step is to find a valid topological order of the graph, such that we can transform the graph dependency into a linear sequence. In this example, we simply hard-code it:<pre class="m-code">const std::vector&lt;std::string&gt; nodes = {&quot;A&quot;, &quot;B&quot;, &quot;C&quot;};</pre></section><section id="GraphPipelineDefineTheStageFunction"><h3><a href="#GraphPipelineDefineTheStageFunction">Define the Stage Function</a></h3>This particular workload does not propagate data directly through the pipeline. In most situations, data is directly stored in a custom graph data structure, and the stage function will just need to know which node to process. For demo&#x27;s sake, we simply output a message to show which stage function is processing which node:<pre class="m-code">// 1st-stage function
void f1(const std::string&amp; node) {
 printf(&quot;f1(%s)\n&quot;, node.c_str());
}

// 3rd-stage function
void f3(const std::string&amp; node) {
 printf(&quot;f3(%s)\n&quot;, node.c_str());
}</pre><aside class="m-note m-info"><h4>Note</h4>A key advantage of Taskflow&#x27;s pipeline programming model is that we do not provide any data abstraction but give users full control over data management, which is typically application-dependent. In an application like this graph processing pipeline, data is managed in a global custom graph data structure, and any data abstraction provided by the library can become a unnecessary overhead.</aside></section><section id="GraphPipelineDefineThePipes"><h3><a href="#GraphPipelineDefineThePipes">Define the Pipes</a></h3>The pipe structure is straightforward. Each pipe encapsulates the corresponding stage function and passes the node into the function argument. The first pipe will cease the pipeline scheduling when it has processed all nodes. To identify which node is being processed at a running pipe, we use <a href="classtf_1_1Pipeflow.html#a295e5d884665c076f4ef5d78139f7c51" class="m-doc">tf::Pipeflow::token</a> to find the index:<pre class="m-code">// first pipe calls f1
tf::Pipe{tf::PipeType::SERIAL, [&amp;](tf::Pipeflow&amp; pf) {
 if(pf.token() == nodes.size()) {
 pf.stop();
 }
 else {
 f1(nodes[pf.token()]);
 }
}},

// second pipe calls f2
tf::Pipe{tf::PipeType::SERIAL, [&amp;](tf::Pipeflow&amp; pf) {
 f2(nodes[pf.token()]);
}},

// third pipe calls f3
tf::Pipe{tf::PipeType::SERIAL, [&amp;](tf::Pipeflow&amp; pf) {
 f3(nodes[pf.token()]);
}}</pre></section><section id="GraphPipelineDefineTheTaskGraph"><h3><a href="#GraphPipelineDefineTheTaskGraph">Define the Task Graph</a></h3>To build up the taskflow for the pipeline, we create a module task with the defined pipeline structure and connect it with two tasks that output helper messages before and after the pipeline:<pre class="m-code">tf::Task init = taskflow.emplace([](){ std::cout &lt;&lt; &quot;ready\n&quot;; })
 .name(&quot;starting pipeline&quot;);
tf::Task task = taskflow.composed_of(pl)
 .name(&quot;pipeline&quot;);
tf::Task stop = taskflow.emplace([](){ std::cout &lt;&lt; &quot;stopped\n&quot;; })
 .name(&quot;pipeline stopped&quot;);
init.precede(task);
task.precede(stop);</pre><div class="m-graph"><svg style="width: 31.700rem; height: 32.700rem;" viewBox="0.00 0.00 317.00 327.00">
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</div></section><section id="GraphPipelineSubmitTheTaskGraph"><h3><a href="#GraphPipelineSubmitTheTaskGraph">Submit the Task Graph</a></h3>Finally, we submit the taskflow to the execution and run it once:<pre class="m-code">executor.run(taskflow).wait();</pre>Three possible outputs are shown below:<pre class="m-console"># possible output 1
ready
f1(A)
f2(A)
f1(B)
f2(B)
f3(A)
f1(C)
f2(C)
f3(B)
f3(C)
stopped

# possible output 2
f1(A)
f2(A)
f3(A)
f1(B)
f2(B)
f3(B)
f1(C)
f2(C)
f3(C)
stopped

# possible output 3
ready
f1(A)
f2(A)
f3(A)
f1(B)
f2(B)
f1(C)
f2(C)
f3(B)
f3(C)
stopped</pre></section></section><section id="GraphPipelineReference"><h2><a href="#GraphPipelineReference">Reference</a></h2>We have applied the graph processing pipeline technique to speed up a circuit analysis problem. Details can be referred to our publication below:<ul><li>Cheng-Hsiang Chiu and Tsung-Wei Huang, &quot;<a href="https://tsung-wei-huang.github.io/papers/dac2022.pdf">Efficient Timing Propagation with Simultaneous Structural and Pipeline Parallelisms</a>,&quot; ACM/IEEE Design Automation Conference (DAC), San Francisco, CA, 2022</li></ul></section>
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一键复制编辑原始数据按行查看历史

twhuang 提交于 2023年05月10日 03:18 +08:00 . fixed old async behavior in documentation

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 <span class="m-breadcrumb"><a href="Examples.html">Learning from Examples</a> &raquo;</span>
 Graph Processing Pipeline
 </h1>
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 <h3>Contents</h3>
 <ul>
 <li><a href="#FormulateTheGraphProcessingPipelineProblem">Formulate the Graph Processing Pipeline Problem</a></li>
 <li>
 <a href="#CreateAGraphProcessingPipeline">Create a Graph Processing Pipeline</a>
 <ul>
 <li><a href="#GraphPipelineFindATopologicalOrderOfTheGraph">Find a Topological Order of the Graph</a></li>
 <li><a href="#GraphPipelineDefineTheStageFunction">Define the Stage Function</a></li>
 <li><a href="#GraphPipelineDefineThePipes">Define the Pipes</a></li>
 <li><a href="#GraphPipelineDefineTheTaskGraph">Define the Task Graph</a></li>
 <li><a href="#GraphPipelineSubmitTheTaskGraph">Submit the Task Graph</a></li>
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 <li><a href="#GraphPipelineReference">Reference</a></li>
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<p>We study a graph processing pipeline that propagates a sequence of linearly dependent tasks over a dependency graph. In this particular workload, we will learn how to transform task graph parallelism into pipeline parallelism.</p><section id="FormulateTheGraphProcessingPipelineProblem"><h2><a href="#FormulateTheGraphProcessingPipelineProblem">Formulate the Graph Processing Pipeline Problem</a></h2><p>Given a directed acyclic graph (DAG), where each node encapsulates a sequence of linearly dependent tasks, namely <em>stage tasks</em>, and each edge represents a dependency between two tasks at the same stages of adjacent nodes. For example, assuming <code>fi(u)</code> represents the <code>i</code><sup>th</sup>-stage task of node <code>u</code>, a dependency from <code>u</code> to <code>v</code> requires <code>fi(u)</code> to run before <code>fi(v)</code>. The following figures shows an example of three stage tasks in a DAG of three nodes (<code>A</code>, <code>B</code>, and <code>C</code>) and two dependencies (<code>A-&gt;B</code> and <code>A-&gt;C</code>):</p><div class="m-graph"><svg style="width: 18.000rem; height: 14.800rem;" viewBox="0.00 0.00 180.00 148.00">
<g transform="scale(1 1) rotate(0) translate(4 144)">
<title>L</title>
<g class="m-node m-flat">
<title>a</title>
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<text text-anchor="start" x="55" y="-128" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">[Node A]</text>
<text text-anchor="start" x="55" y="-117" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 1: f1(A)</text>
<text text-anchor="start" x="55" y="-106" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 2: f2(A)</text>
<text text-anchor="start" x="55" y="-95" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 3: f3(A)</text>
</g>
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<text text-anchor="start" x="8" y="-40" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">[Node B]</text>
<text text-anchor="start" x="8" y="-29" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 1: f1(B)</text>
<text text-anchor="start" x="8" y="-18" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 2: f2(B)</text>
<text text-anchor="start" x="8" y="-7" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 3: f3(B)</text>
</g>
<g class="m-edge">
<title>a&#45;&gt;b</title>
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<polygon points="60.228,-59.2529 52.4296,-52.081 54.0535,-62.5507 60.228,-59.2529"/>
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<title>c</title>
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<text text-anchor="start" x="103" y="-40" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">[Node C]</text>
<text text-anchor="start" x="103" y="-29" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 1: f1(C)</text>
<text text-anchor="start" x="103" y="-18" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 2: f2(C)</text>
<text text-anchor="start" x="103" y="-7" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">Step 3: f3(C)</text>
</g>
<g class="m-edge">
<title>a&#45;&gt;c</title>
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</div><p>While we can directly create a taskflow for the DAG (i.e., each task in the taskflow runs <code>f1</code>, <code>f2</code>, and <code>f3</code> sequentially), we can describe the parallelism as a three-stage pipeline that propagates a topological order of the DAG through three stage tasks. Consider a valid topological order of this DAG, <code>A, B, C</code>, its pipeline parallelism can be illustrated in the following figure:</p><div class="m-graph"><svg style="width: 20.600rem; height: 33.200rem;" viewBox="0.00 0.00 206.00 332.00">
<g transform="scale(1 1) rotate(0) translate(4 328)">
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<title>f1_A</title>
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<g class="m-node m-flat">
<title>f1_B</title>
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<g class="m-edge">
<title>f1_A&#45;&gt;f1_B</title>
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<title>f2_A</title>
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<g class="m-node m-flat">
<title>f2_B</title>
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<g class="m-edge">
<title>f2_A&#45;&gt;f2_B</title>
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<g class="m-node m-flat">
<title>f3_A</title>
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<g class="m-node m-flat">
<title>f3_B</title>
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<text text-anchor="middle" x="171" y="-87.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f3(B)</text>
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<g class="m-edge">
<title>f3_A&#45;&gt;f3_B</title>
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<g class="m-edge">
<title>f1_B&#45;&gt;f2_A</title>
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<g class="m-node m-flat">
<title>f1_C</title>
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<g class="m-edge">
<title>f1_B&#45;&gt;f1_C</title>
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<g class="m-edge">
<title>f2_B&#45;&gt;f3_A</title>
<path d="M126.2813,-162C132.104,-162 137.9268,-162 143.7495,-162"/>
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<g class="m-node m-flat">
<title>f2_C</title>
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</g>
<g class="m-edge">
<title>f2_B&#45;&gt;f2_C</title>
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<polygon points="102.5001,-118.4132 99,-108.4133 95.5001,-118.4133 102.5001,-118.4132"/>
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<g class="m-node m-flat">
<title>f3_C</title>
<polygon points="198,-36 144,-36 144,0 198,0 198,-36"/>
<text text-anchor="middle" x="171" y="-15.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f3(C)</text>
</g>
<g class="m-edge">
<title>f3_B&#45;&gt;f3_C</title>
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<polygon points="174.5001,-46.4132 171,-36.4133 167.5001,-46.4133 174.5001,-46.4132"/>
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<g class="m-edge">
<title>f1_C&#45;&gt;f2_B</title>
<path d="M54.2813,-162C60.104,-162 65.9268,-162 71.7495,-162"/>
</g>
<g class="m-edge">
<title>f2_C&#45;&gt;f3_B</title>
<path d="M126.2813,-90C132.104,-90 137.9268,-90 143.7495,-90"/>
</g>
</g>
</svg>
</div><p>At the beginning, <code>f1(A)</code> runs first. When <code>f1(A)</code> completes, it moves on to <code>f2(A)</code> and, meanwhile, <code>f1(B)</code> can start to run together with <code>f2(A)</code>, and so on so forth. The straight line represents two parallel tasks that can overlap in time in the pipeline. For example, <code>f3(A)</code>, <code>f2(B)</code>, and <code>f1(C)</code> can run simultaneously. The following figures shows the task dependency graph of this pipeline workload:</p><div class="m-graph"><svg style="width: 20.600rem; height: 18.800rem;" viewBox="0.00 0.00 206.00 188.00">
<g transform="scale(1 1) rotate(0) translate(4 184)">
<title>R</title>
<g class="m-node m-flat">
<title>f1_A</title>
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<text text-anchor="middle" x="27" y="-159.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f1(A)</text>
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<g class="m-node m-flat">
<title>f1_B</title>
<polygon points="126,-180 72,-180 72,-144 126,-144 126,-180"/>
<text text-anchor="middle" x="99" y="-159.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f1(B)</text>
</g>
<g class="m-edge">
<title>f1_A&#45;&gt;f1_B</title>
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<g class="m-node m-flat">
<title>f2_A</title>
<polygon points="54,-108 0,-108 0,-72 54,-72 54,-108"/>
<text text-anchor="middle" x="27" y="-87.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f2(A)</text>
</g>
<g class="m-edge">
<title>f1_A&#45;&gt;f2_A</title>
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<polygon points="30.5001,-118.4132 27,-108.4133 23.5001,-118.4133 30.5001,-118.4132"/>
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<g class="m-node m-flat">
<title>f1_C</title>
<polygon points="198,-180 144,-180 144,-144 198,-144 198,-180"/>
<text text-anchor="middle" x="171" y="-159.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f1(C)</text>
</g>
<g class="m-edge">
<title>f1_B&#45;&gt;f1_C</title>
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<polygon points="133.7495,-165.5001 143.7495,-162 133.7495,-158.5001 133.7495,-165.5001"/>
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<g class="m-node m-flat">
<title>f2_B</title>
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<text text-anchor="middle" x="99" y="-87.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f2(B)</text>
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<g class="m-edge">
<title>f1_B&#45;&gt;f2_B</title>
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<polygon points="102.5001,-118.4132 99,-108.4133 95.5001,-118.4133 102.5001,-118.4132"/>
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<g class="m-node m-flat">
<title>f2_C</title>
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<text text-anchor="middle" x="171" y="-87.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f2(C)</text>
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<g class="m-edge">
<title>f1_C&#45;&gt;f2_C</title>
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<g class="m-edge">
<title>f2_A&#45;&gt;f2_B</title>
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<polygon points="61.7495,-93.5001 71.7495,-90 61.7495,-86.5001 61.7495,-93.5001"/>
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<g class="m-node m-flat">
<title>f3_A</title>
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<text text-anchor="middle" x="27" y="-15.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f3(A)</text>
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<g class="m-edge">
<title>f2_A&#45;&gt;f3_A</title>
<path d="M27,-71.8314C27,-64.131 27,-54.9743 27,-46.4166"/>
<polygon points="30.5001,-46.4132 27,-36.4133 23.5001,-46.4133 30.5001,-46.4132"/>
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<g class="m-edge">
<title>f2_B&#45;&gt;f2_C</title>
<path d="M126.2813,-90C128.7377,-90 131.1942,-90 133.6507,-90"/>
<polygon points="133.7495,-93.5001 143.7495,-90 133.7495,-86.5001 133.7495,-93.5001"/>
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<g class="m-node m-flat">
<title>f3_B</title>
<polygon points="126,-36 72,-36 72,0 126,0 126,-36"/>
<text text-anchor="middle" x="99" y="-15.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f3(B)</text>
</g>
<g class="m-edge">
<title>f2_B&#45;&gt;f3_B</title>
<path d="M99,-71.8314C99,-64.131 99,-54.9743 99,-46.4166"/>
<polygon points="102.5001,-46.4132 99,-36.4133 95.5001,-46.4133 102.5001,-46.4132"/>
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<g class="m-node m-flat">
<title>f3_C</title>
<polygon points="198,-36 144,-36 144,0 198,0 198,-36"/>
<text text-anchor="middle" x="171" y="-15.5" font-family="Helvetica,sans-Serif" font-size="10.00" fill="#000000">f3(C)</text>
</g>
<g class="m-edge">
<title>f2_C&#45;&gt;f3_C</title>
<path d="M171,-71.8314C171,-64.131 171,-54.9743 171,-46.4166"/>
<polygon points="174.5001,-46.4132 171,-36.4133 167.5001,-46.4133 174.5001,-46.4132"/>
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<g class="m-edge">
<title>f3_A&#45;&gt;f3_B</title>
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<g class="m-edge">
<title>f3_B&#45;&gt;f3_C</title>
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<polygon points="133.7495,-21.5001 143.7495,-18 133.7495,-14.5001 133.7495,-21.5001"/>
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</div><p>As we can see, tasks in diagonal lines (lower-left to upper-right) can run in parallel. This type of parallelism is also referred to as <em>wavefront</em> parallelism, which sweeps parallel elements in a diagonal direction.</p><aside class="m-note m-info"><h4>Note</h4><p>Depending on the graph size and the number of stage tasks, task graph parallelism and pipeline parallelism can bring very different performance results. For example, a small graph will a long chain of stage tasks may perform better with pipeline parallelism than task graph parallelism, and vice versa.</p></aside></section><section id="CreateAGraphProcessingPipeline"><h2><a href="#CreateAGraphProcessingPipeline">Create a Graph Processing Pipeline</a></h2><p>Using the example from the previous section, we create a three-stage pipeline that encapsulates the three stage tasks (<code>f1, f2, f3</code>) in three pipes. By finding a topological order of the graph, we can transform the node dependency into a sequence of linearly dependent data tokens to feed into the pipeline. The overall implementation is shown below:</p><pre class="m-code"><span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;taskflow/taskflow.hpp&gt;</span><span class="cp"></span>
<span class="cp">#include</span><span class="w"> </span><span class="cpf">&lt;taskflow/algorithm/pipeline.hpp&gt;</span><span class="cp"></span>

<span class="c1">// 1st-stage function</span>
<span class="kt">void</span><span class="w"> </span><span class="nf">f1</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&amp;</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;f1(%s)</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">c_str</span><span class="p">());</span><span class="w"></span>
<span class="p">}</span><span class="w"></span>

<span class="c1">// 2nd-stage function</span>
<span class="kt">void</span><span class="w"> </span><span class="nf">f2</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&amp;</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;f2(%s)</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">c_str</span><span class="p">());</span><span class="w"></span>
<span class="p">}</span><span class="w"></span>

<span class="c1">// 3rd-stage function</span>
<span class="kt">void</span><span class="w"> </span><span class="nf">f3</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&amp;</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;f3(%s)</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">c_str</span><span class="p">());</span><span class="w"></span>
<span class="p">}</span><span class="w"></span>

<span class="kt">int</span><span class="w"> </span><span class="nf">main</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"></span>

<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Taskflow</span><span class="w"> </span><span class="n">taskflow</span><span class="p">(</span><span class="s">&quot;graph processing pipeline&quot;</span><span class="p">);</span><span class="w"></span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Executor</span><span class="w"> </span><span class="n">executor</span><span class="p">;</span><span class="w"></span>

<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="kt">size_t</span><span class="w"> </span><span class="n">num_lines</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"></span>
<span class="w"> </span>
<span class="w"> </span><span class="c1">// a topological order of the graph</span>
<span class="w"> </span><span class="c1">// |-&gt; B</span>
<span class="w"> </span><span class="c1">// A--|</span>
<span class="w"> </span><span class="c1">// |-&gt; C</span>
<span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="s">&quot;A&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;B&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;C&quot;</span><span class="p">};</span><span class="w"></span>

<span class="w"> </span><span class="c1">// the pipeline consists of three serial pipes</span>
<span class="w"> </span><span class="c1">// and up to two concurrent scheduling tokens</span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Pipeline</span><span class="w"> </span><span class="n">pl</span><span class="p">(</span><span class="n">num_lines</span><span class="p">,</span><span class="w"></span>

<span class="w"> </span><span class="c1">// first pipe calls f1</span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Pipe</span><span class="p">{</span><span class="n">tf</span><span class="o">::</span><span class="n">PipeType</span><span class="o">::</span><span class="n">SERIAL</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="n">tf</span><span class="o">::</span><span class="n">Pipeflow</span><span class="o">&amp;</span><span class="w"> </span><span class="n">pf</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="k">if</span><span class="p">(</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">pf</span><span class="p">.</span><span class="n">stop</span><span class="p">();</span><span class="w"></span>
<span class="w"> </span><span class="p">}</span><span class="w"></span>
<span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">f1</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()]);</span><span class="w"></span>
<span class="w"> </span><span class="p">}</span><span class="w"></span>
<span class="w"> </span><span class="p">}},</span><span class="w"></span>
<span class="w"> </span>
<span class="w"> </span><span class="c1">// second pipe calls f2</span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Pipe</span><span class="p">{</span><span class="n">tf</span><span class="o">::</span><span class="n">PipeType</span><span class="o">::</span><span class="n">SERIAL</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="n">tf</span><span class="o">::</span><span class="n">Pipeflow</span><span class="o">&amp;</span><span class="w"> </span><span class="n">pf</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">f2</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()]);</span><span class="w"></span>
<span class="w"> </span><span class="p">}},</span><span class="w"></span>

<span class="w"> </span><span class="c1">// third pipe calls f3</span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Pipe</span><span class="p">{</span><span class="n">tf</span><span class="o">::</span><span class="n">PipeType</span><span class="o">::</span><span class="n">SERIAL</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="n">tf</span><span class="o">::</span><span class="n">Pipeflow</span><span class="o">&amp;</span><span class="w"> </span><span class="n">pf</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">f3</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()]);</span><span class="w"></span>
<span class="w"> </span><span class="p">}}</span><span class="w"></span>
<span class="w"> </span><span class="p">);</span><span class="w"></span>

<span class="w"> </span><span class="c1">// build the pipeline graph using composition</span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">init</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">emplace</span><span class="p">([](){</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;ready</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span><span class="w"> </span><span class="p">})</span><span class="w"></span>
<span class="w"> </span><span class="p">.</span><span class="n">name</span><span class="p">(</span><span class="s">&quot;starting pipeline&quot;</span><span class="p">);</span><span class="w"></span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">task</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">composed_of</span><span class="p">(</span><span class="n">pl</span><span class="p">)</span><span class="w"></span>
<span class="w"> </span><span class="p">.</span><span class="n">name</span><span class="p">(</span><span class="s">&quot;pipeline&quot;</span><span class="p">);</span><span class="w"></span>
<span class="w"> </span><span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">stop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">emplace</span><span class="p">([](){</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;stopped</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span><span class="w"> </span><span class="p">})</span><span class="w"></span>
<span class="w"> </span><span class="p">.</span><span class="n">name</span><span class="p">(</span><span class="s">&quot;pipeline stopped&quot;</span><span class="p">);</span><span class="w"></span>

<span class="w"> </span><span class="c1">// create task dependency</span>
<span class="w"> </span><span class="n">init</span><span class="p">.</span><span class="n">precede</span><span class="p">(</span><span class="n">task</span><span class="p">);</span><span class="w"></span>
<span class="w"> </span><span class="n">task</span><span class="p">.</span><span class="n">precede</span><span class="p">(</span><span class="n">stop</span><span class="p">);</span><span class="w"></span>

<span class="w"> </span><span class="c1">// dump the pipeline graph structure (with composition)</span>
<span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">dump</span><span class="p">(</span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="p">);</span><span class="w"></span>

<span class="w"> </span><span class="c1">// run the pipeline</span>
<span class="w"> </span><span class="n">executor</span><span class="p">.</span><span class="n">run</span><span class="p">(</span><span class="n">taskflow</span><span class="p">).</span><span class="n">wait</span><span class="p">();</span><span class="w"></span>

<span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"></span>
<span class="p">}</span><span class="w"></span></pre><section id="GraphPipelineFindATopologicalOrderOfTheGraph"><h3><a href="#GraphPipelineFindATopologicalOrderOfTheGraph">Find a Topological Order of the Graph</a></h3><p>The first step is to find a valid topological order of the graph, such that we can transform the graph dependency into a linear sequence. In this example, we simply hard-code it:</p><pre class="m-code"><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="s">&quot;A&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;B&quot;</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;C&quot;</span><span class="p">};</span><span class="w"></span></pre></section><section id="GraphPipelineDefineTheStageFunction"><h3><a href="#GraphPipelineDefineTheStageFunction">Define the Stage Function</a></h3><p>This particular workload does not propagate data directly through the pipeline. In most situations, data is directly stored in a custom graph data structure, and the stage function will just need to know which node to process. For demo&#x27;s sake, we simply output a message to show which stage function is processing which node:</p><pre class="m-code"><span class="c1">// 1st-stage function</span>
<span class="kt">void</span><span class="w"> </span><span class="nf">f1</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&amp;</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;f1(%s)</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">c_str</span><span class="p">());</span><span class="w"></span>
<span class="p">}</span><span class="w"></span>

<span class="c1">// 2nd-stage function</span>
<span class="kt">void</span><span class="w"> </span><span class="nf">f2</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&amp;</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;f2(%s)</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">c_str</span><span class="p">());</span><span class="w"></span>
<span class="p">}</span><span class="w"></span>

<span class="c1">// 3rd-stage function</span>
<span class="kt">void</span><span class="w"> </span><span class="nf">f3</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">string</span><span class="o">&amp;</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;f3(%s)</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="n">c_str</span><span class="p">());</span><span class="w"></span>
<span class="p">}</span><span class="w"></span></pre><aside class="m-note m-info"><h4>Note</h4><p>A key advantage of Taskflow&#x27;s pipeline programming model is that we do not provide any data abstraction but give users full control over data management, which is typically application-dependent. In an application like this graph processing pipeline, data is managed in a global custom graph data structure, and any data abstraction provided by the library can become a unnecessary overhead.</p></aside></section><section id="GraphPipelineDefineThePipes"><h3><a href="#GraphPipelineDefineThePipes">Define the Pipes</a></h3><p>The pipe structure is straightforward. Each pipe encapsulates the corresponding stage function and passes the node into the function argument. The first pipe will cease the pipeline scheduling when it has processed all nodes. To identify which node is being processed at a running pipe, we use <a href="classtf_1_1Pipeflow.html#a295e5d884665c076f4ef5d78139f7c51" class="m-doc">tf::<wbr />Pipeflow::<wbr />token</a> to find the index:</p><pre class="m-code"><span class="c1">// first pipe calls f1</span>
<span class="n">tf</span><span class="o">::</span><span class="n">Pipe</span><span class="p">{</span><span class="n">tf</span><span class="o">::</span><span class="n">PipeType</span><span class="o">::</span><span class="n">SERIAL</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="n">tf</span><span class="o">::</span><span class="n">Pipeflow</span><span class="o">&amp;</span><span class="w"> </span><span class="n">pf</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="k">if</span><span class="p">(</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nodes</span><span class="p">.</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">pf</span><span class="p">.</span><span class="n">stop</span><span class="p">();</span><span class="w"></span>
<span class="w"> </span><span class="p">}</span><span class="w"></span>
<span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">f1</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()]);</span><span class="w"></span>
<span class="w"> </span><span class="p">}</span><span class="w"></span>
<span class="p">}},</span><span class="w"></span>

<span class="c1">// second pipe calls f2</span>
<span class="n">tf</span><span class="o">::</span><span class="n">Pipe</span><span class="p">{</span><span class="n">tf</span><span class="o">::</span><span class="n">PipeType</span><span class="o">::</span><span class="n">SERIAL</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="n">tf</span><span class="o">::</span><span class="n">Pipeflow</span><span class="o">&amp;</span><span class="w"> </span><span class="n">pf</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">f2</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()]);</span><span class="w"></span>
<span class="p">}},</span><span class="w"></span>

<span class="c1">// third pipe calls f3</span>
<span class="n">tf</span><span class="o">::</span><span class="n">Pipe</span><span class="p">{</span><span class="n">tf</span><span class="o">::</span><span class="n">PipeType</span><span class="o">::</span><span class="n">SERIAL</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="o">&amp;</span><span class="p">](</span><span class="n">tf</span><span class="o">::</span><span class="n">Pipeflow</span><span class="o">&amp;</span><span class="w"> </span><span class="n">pf</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"></span>
<span class="w"> </span><span class="n">f3</span><span class="p">(</span><span class="n">nodes</span><span class="p">[</span><span class="n">pf</span><span class="p">.</span><span class="n">token</span><span class="p">()]);</span><span class="w"></span>
<span class="p">}}</span><span class="w"></span></pre></section><section id="GraphPipelineDefineTheTaskGraph"><h3><a href="#GraphPipelineDefineTheTaskGraph">Define the Task Graph</a></h3><p>To build up the taskflow for the pipeline, we create a module task with the defined pipeline structure and connect it with two tasks that output helper messages before and after the pipeline:</p><pre class="m-code"><span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">init</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">emplace</span><span class="p">([](){</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;ready</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span><span class="w"> </span><span class="p">})</span><span class="w"></span>
<span class="w"> </span><span class="p">.</span><span class="n">name</span><span class="p">(</span><span class="s">&quot;starting pipeline&quot;</span><span class="p">);</span><span class="w"></span>
<span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">task</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">composed_of</span><span class="p">(</span><span class="n">pl</span><span class="p">)</span><span class="w"></span>
<span class="w"> </span><span class="p">.</span><span class="n">name</span><span class="p">(</span><span class="s">&quot;pipeline&quot;</span><span class="p">);</span><span class="w"></span>
<span class="n">tf</span><span class="o">::</span><span class="n">Task</span><span class="w"> </span><span class="n">stop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">taskflow</span><span class="p">.</span><span class="n">emplace</span><span class="p">([](){</span><span class="w"> </span><span class="n">std</span><span class="o">::</span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;stopped</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span><span class="w"> </span><span class="p">})</span><span class="w"></span>
<span class="w"> </span><span class="p">.</span><span class="n">name</span><span class="p">(</span><span class="s">&quot;pipeline stopped&quot;</span><span class="p">);</span><span class="w"></span>
<span class="n">init</span><span class="p">.</span><span class="n">precede</span><span class="p">(</span><span class="n">task</span><span class="p">);</span><span class="w"></span>
<span class="n">task</span><span class="p">.</span><span class="n">precede</span><span class="p">(</span><span class="n">stop</span><span class="p">);</span><span class="w"></span></pre><div class="m-graph"><svg style="width: 31.700rem; height: 32.700rem;" viewBox="0.00 0.00 317.00 327.00">
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</div></section><section id="GraphPipelineSubmitTheTaskGraph"><h3><a href="#GraphPipelineSubmitTheTaskGraph">Submit the Task Graph</a></h3><p>Finally, we submit the taskflow to the execution and run it once:</p><pre class="m-code"><span class="n">executor</span><span class="p">.</span><span class="n">run</span><span class="p">(</span><span class="n">taskflow</span><span class="p">).</span><span class="n">wait</span><span class="p">();</span><span class="w"></span></pre><p>Three possible outputs are shown below:</p><pre class="m-console"><span class="gp"># </span>possible output <span class="m">1</span>
<span class="go">ready</span>
<span class="go">f1(A)</span>
<span class="go">f2(A)</span>
<span class="go">f1(B)</span>
<span class="go">f2(B)</span>
<span class="go">f3(A)</span>
<span class="go">f1(C)</span>
<span class="go">f2(C)</span>
<span class="go">f3(B)</span>
<span class="go">f3(C)</span>
<span class="go">stopped</span>

<span class="gp"># </span>possible output <span class="m">2</span>
<span class="go">f1(A)</span>
<span class="go">f2(A)</span>
<span class="go">f3(A)</span>
<span class="go">f1(B)</span>
<span class="go">f2(B)</span>
<span class="go">f3(B)</span>
<span class="go">f1(C)</span>
<span class="go">f2(C)</span>
<span class="go">f3(C)</span>
<span class="go">stopped</span>

<span class="gp"># </span>possible output <span class="m">3</span>
<span class="go">ready</span>
<span class="go">f1(A)</span>
<span class="go">f2(A)</span>
<span class="go">f3(A)</span>
<span class="go">f1(B)</span>
<span class="go">f2(B)</span>
<span class="go">f1(C)</span>
<span class="go">f2(C)</span>
<span class="go">f3(B)</span>
<span class="go">f3(C)</span>
<span class="go">stopped</span></pre></section></section><section id="GraphPipelineReference"><h2><a href="#GraphPipelineReference">Reference</a></h2><p>We have applied the graph processing pipeline technique to speed up a circuit analysis problem. Details can be referred to our publication below:</p><ul><li>Cheng-Hsiang Chiu and Tsung-Wei Huang, &quot;<a href="https://tsung-wei-huang.github.io/papers/dac2022.pdf">Efficient Timing Propagation with Simultaneous Structural and Pipeline Parallelisms</a>,&quot; <em>ACM/IEEE Design Automation Conference (DAC)</em>, San Francisco, CA, 2022</li></ul></section>
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