Understanding the SIMD Efficiency of Graph Traversal on GPUYichao Cheng, Hong An, Zhitao Chen, Feng Li, Zhaohui Wang, Xia Jiang and Yi Peng

University of Science and Technology of China

Breadth-first Search (BFS)

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Breadth-first Search (BFS)

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BFS_Iteration:for u ∈ Current Frontier for v ∈ u’ s neighbors do if v has not been labeled label v put v in Next Frontier

Application of BFS• Many datasets in real world are represented by graph• VLSI circuits• Social relationship• Road connections

• Primitive for building complex algorithms• Path-finding• Belief propagation• Points-to Analysis (PTA)

The Problem•GPU relies on high SIMD lanes occupancy to boost performance • 100% efficiency is achieved only if all SIMD lanes fall in the same path

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Do_something_common();If (thread_id > 5) { do_something_red(); } else { do something_blue();}

100% utilization

The Problem•GPU relies on high SIMD lanes occupancy to boost performance • 100% efficiency is achieved only if all SIMD lanes fall in the same path

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37.5% utilization

Do_something_common();If (thread_id > 5) { do_something_red(); } else { do something_blue();}

The Problem•GPU relies on high SIMD lanes occupancy to boost performance • 100% efficiency is achieved only if all SIMD lanes fall in the same path

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62.5% utilization

Do_something_common();If (thread_id > 5) { do_something_red(); } else { do something_blue();}

Traditional ImplementationGPU_BFS_Iteration u = C[tid] for v ∈ u’ s neighbors do

end for

The # of sub-iterations depends on

the size of u ’s adjacent list

task 1 = 4 sub-iterations

task 2 = 2 sub-iterations

…

Visualizing the Irregularity

vertex range < 8

Highly skewedoutlier exists

irregular but concentrate

distributedbetween a wide rage

Alternative Way• Assign each task with a warp of threads• Vectorize the sub-iterations!

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So, what’s the relationship between graph topology and SIMD efficiency?

Topology and Utilization• Assign each vertex with a group of threads

Thread Warp Group

task 1 = 2 sub-iterationstask 2 = 1 sub-iteration

Topology and Utilization

Divide the SIMD underutilization into two parts• InteR-group Underutilization (UR)

• IntrA-group Underutilization (UA)

SIMD Window

Conclusions From the Model

•UR is induced by the heterogeneity of workloads• Affected by the graph topology

•UR is sensitive to the group size (S)• Large logical SIMD window can narrow the gap• When S = 32, UR = 0

•UA is determined by the intrinsic irregularity of vertex degree• It can be limited by shrink the S• When S = 1, UA = 0

•UR and UA can convert to each other

Comparing Different Mapping Strategies

Expansion Rate (ME/s)

Scalability

good

poor

low high

Evaluating the SIMD Efficiency•Metrics derived from the model:

UR = inter-group underutilizationUA = intra-group underutilizationME = mapping efficiency UR + UA + ME = 100%

• Captures utilization trend with increasing S

Explaining the Result

Expansion Rate (ME/s)

Scalability

good

poor

low high

alleviate the UR ， introducing minor UA

Explaining the Result

Expansion Rate (ME/s)

Scalability

good

poor

low high

ME in a high level (~80%)

Explaining the Result

Expansion Rate (ME/s)

Scalability

good

poor

low high

outweighed by the fast-growing UA

Explaining the Result

Expansion Rate (ME/s)

Scalability

good

poor

low high

do little help to UR but lead to severe UA

Conclusion• Study the link between graph topo & hardware util• Present a model for analyzing the components of SIMD underutilization• Discover that the SIMD are wasted due to:•Develop 3 metrics for quantifying SIMD efficiency• Provide a foundation for developing techniques of static analysis and runtime optimization

imbalance of vertex degree distribution heterogeneity of

each vertex degree

Q&A