GraphProcessingPipeline

# Graph Processing Pipeline

Formulate the Graph Processing Pipeline Problem
GraphProcessingPipeline_1FormulateTheGraphProcessingPipelineProblem
Create a Graph Processing Pipeline
GraphProcessingPipeline_1CreateAGraphProcessingPipeline
Find a Topological Order of the Graph
GraphProcessingPipeline_1GraphPipelineFindATopologicalOrderOfTheGraph
Define the Stage Function
GraphProcessingPipeline_1GraphPipelineDefineTheStageFunction
Define the Pipes
GraphProcessingPipeline_1GraphPipelineDefineThePipes
Define the Task Graph
GraphProcessingPipeline_1GraphPipelineDefineTheTaskGraph
Submit the Task Graph
GraphProcessingPipeline_1GraphPipelineSubmitTheTaskGraph
Reference
GraphProcessingPipeline_1GraphPipelineReference

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.

# Formulate the Graph Processing Pipeline Problem

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 `fi(u)` represents the `i`th-stage task of node `u`, a dependency from `u` to `v` requires `fi(u)` to run before `fi(v)`. The following figures shows an example of three stage tasks in a DAG of three nodes (`A`, `B`, and `C`) and two dependencies (`A->B` and `A->C`):

While we can directly create a taskflow for the DAG (i.e., each task in the taskflow runs `f1`, `f2`, and `f3` 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, `A, B, C`, its pipeline parallelism can be illustrated in the following figure:

At the beginning, `f1(A)` runs first. When `f1(A)` completes, it moves on to `f2(A)` and, meanwhile, `f1(B)` can start to run together with `f2(A)`, and so on so forth. The straight line represents two parallel tasks that can overlap in time in the pipeline. For example, `f3(A)`, `f2(B)`, and `f1(C)` can run simultaneously. The following figures shows the task dependency graph of this pipeline workload:

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.

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.

# Create a Graph Processing Pipeline

Using the example from the previous section, we create a three-stage pipeline that encapsulates the three stage tasks (`f1, f2, f3`) 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:

    #include<taskflow/taskflow.hpp>
    #include<taskflow/algorithm/pipeline.hpp>

    //1st-stagefunction
    voidf1(conststd::string&node){
    printf("f1(%s)\n",node.c_str());
    }

    //2nd-stagefunction
    voidf2(conststd::string&node){
    printf("f2(%s)\n",node.c_str());
    }

    //3rd-stagefunction
    voidf3(conststd::string&node){
    printf("f3(%s)\n",node.c_str());
    }

    intmain(){

    tf::Taskflowtaskflow("graphprocessingpipeline");
    tf::Executorexecutor;

    constsize_tnum_lines=2;

    //atopologicalorderofthegraph
    //|->B
    //A--|
    //|->C
    conststd::vector<std::string>nodes={"A","B","C"};

    //thepipelineconsistsofthreeserialpipes
    //anduptotwoconcurrentschedulingtokens
    tf::Pipelinepl(num_lines,

    //firstpipecallsf1
    tf::Pipe{tf::PipeType::SERIAL,[&](tf::Pipeflow&pf){
    if(pf.token()==nodes.size()){
    pf.stop();
    }
    else{
    f1(nodes[pf.token()]);
    }
    }},

    //secondpipecallsf2
    tf::Pipe{tf::PipeType::SERIAL,[&](tf::Pipeflow&pf){
    f2(nodes[pf.token()]);
    }},

    //thirdpipecallsf3
    tf::Pipe{tf::PipeType::SERIAL,[&](tf::Pipeflow&pf){
    f3(nodes[pf.token()]);
    }}
    );

    //buildthepipelinegraphusingcomposition
    tf::Taskinit=taskflow.emplace([](){std::cout<<"ready\n";})
    .name("startingpipeline");
    tf::Tasktask=taskflow.composed_of(pl)
    .name("pipeline");
    tf::Taskstop=taskflow.emplace([](){std::cout<<"stopped\n";})
    .name("pipelinestopped");

    //createtaskdependency
    init.precede(task);
    task.precede(stop);

    //dumpthepipelinegraphstructure(withcomposition)
    taskflow.dump(std::cout);

    //runthepipeline
    executor.run(taskflow).wait();

    return0;
    }

## Find a Topological Order of the Graph

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:

    conststd::vector<std::string>nodes={"A","B","C"};

## Define the Stage Function

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's sake, we simply output a message to show which stage function is processing which node:

    //1st-stagefunction
    voidf1(conststd::string&node){
    printf("f1(%s)\n",node.c_str());
    }

    //2nd-stagefunction
    voidf2(conststd::string&node){
    printf("f2(%s)\n",node.c_str());
    }

    //3rd-stagefunction
    voidf3(conststd::string&node){
    printf("f3(%s)\n",node.c_str());
    }

A key advantage of Taskflow'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.

## Define the Pipes

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 tf::Pipeflow::token to find the index:

    //firstpipecallsf1
    tf::Pipe{tf::PipeType::SERIAL,[&](tf::Pipeflow&pf){
    if(pf.token()==nodes.size()){
    pf.stop();
    }
    else{
    f1(nodes[pf.token()]);
    }
    }},

    //secondpipecallsf2
    tf::Pipe{tf::PipeType::SERIAL,[&](tf::Pipeflow&pf){
    f2(nodes[pf.token()]);
    }},

    //thirdpipecallsf3
    tf::Pipe{tf::PipeType::SERIAL,[&](tf::Pipeflow&pf){
    f3(nodes[pf.token()]);
    }}

## Define the Task Graph

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:

    tf::Taskinit=taskflow.emplace([](){std::cout<<"ready\n";})
    .name("startingpipeline");
    tf::Tasktask=taskflow.composed_of(pl)
    .name("pipeline");
    tf::Taskstop=taskflow.emplace([](){std::cout<<"stopped\n";})
    .name("pipelinestopped");
    init.precede(task);
    task.precede(stop);

## Submit the Task Graph

Finally, we submit the taskflow to the execution and run it once:

    executor.run(taskflow).wait();

Three possible outputs are shown below:

    #possibleoutput1
    ready
    f1(A)
    f2(A)
    f1(B)
    f2(B)
    f3(A)
    f1(C)
    f2(C)
    f3(B)
    f3(C)
    stopped

    #possibleoutput2
    f1(A)
    f2(A)
    f3(A)
    f1(B)
    f2(B)
    f3(B)
    f1(C)
    f2(C)
    f3(C)
    stopped

    #possibleoutput3
    ready
    f1(A)
    f2(A)
    f3(A)
    f1(B)
    f2(B)
    f1(C)
    f2(C)
    f3(B)
    f3(C)
    stopped

# Reference

We have applied the graph processing pipeline technique to speed up a circuit analysis problem. Details can be referred to our publication below:

- Cheng-Hsiang Chiu and Tsung-Wei Huang, "Efficient Timing Propagation with Simultaneous Structural and Pipeline Parallelisms," ACM/IEEE Design Automation Conference (DAC), San Francisco, CA, 2022