the Xeon Phi Jie Lin, Qingbo Wu, Yusong Tan, Jie Yu, Qi Zhang, - - PowerPoint PPT Presentation

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the Xeon Phi Jie Lin, Qingbo Wu, Yusong Tan, Jie Yu, Qi Zhang, - - PowerPoint PPT Presentation

Jun 19, 2023 281 likes •524 views

MicRun A Framework for Scale-free Graph Algorithms on SIMD Architecture of the Xeon Phi Jie Lin, Qingbo Wu, Yusong Tan, Jie Yu, Qi Zhang, Xiaoling Li and Lei Luo College of Computer National University of Defense Technology 10/7/2017

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MicRun：A Framework for Scale-free Graph Algorithms on SIMD Architecture of the Xeon Phi

Jie Lin, Qingbo Wu, Yusong Tan, Jie Yu, Qi Zhang, Xiaoling Li and Lei Luo College of Computer National University of Defense Technology

10/7/2017

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Section 1 Backgrounds & Motivation

– Scale-free Graphs & Graph Algorithms – The Xeon Phi Architecture – Bucket Grouping Module – Auto-tuning Module

Section 2 The MicRun Framework Section 3 Experiments & Conclusions

Outline

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Section 1 Backgrounds & Motivation

– Scale-free Graphs & Graph Algorithms – The Xeon Phi Architecture – Bucket Grouping Module – Auto-tuning Module

Section 2 The MicRun Framework Section 3 Experiments & Conclusions

Outline

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  • Scale-free Graphs are Widely Used

− Social Networks Applications − Chemical Molecular Structures − Reference Citations

  • Features of Scale-free Graphs

− The Sparsity Characteristic of Graphs − The Connectivity of Vertices Follows Power-law Distribution

10 10 1 10 2 10 3 10 4 10 10 1 10 2 10 3 10 4 10 5 Degree Number of Vertices 10 10 1 10 2 10 3 10 10 2 10 4 10 6 Degree Number of Vertices

(a) Higgs-twitter (b) Soc-pokec

Backgrounds & Motivation

y = x-γ

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  • Graph Algorithms

− Load values of source vertices − Load values of edges − Compute

(e.g. Addition Minimum et.)

− Update destination vertices

Backgrounds & Motivation

  • Sequential computation steps
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  • The Xeon Phi Architecture

− Architecture: Many Integrated Core (MIC) − 512-bit VPU and four hyper-threads supported − Frequency is more than 1.50GHz − Memory (GDDR5) is more than 8GB − 57-72 cores with optimized KNC Instruction set − Connect to CPU with PCIE

Backgrounds & Motivation

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Backgrounds & Motivation

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  • Challenges of Executing Graph Algorithms on Phi

− SIMD access locality influenced by access range − Write conflicts can occur in SIMD Parallelism

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  • Tiling-and-Grouping Strategy is Commonly Used

− Tiling  Enhance the data locality − Grouping  Remove Parallel conflict − Related Citations

 Efficient Parallel Graph Processing over CPU and MIC (Chen et al. CGO. 2016)  Reusing Data Reorganization of graph

  • Applications. (Jiang et al. IPDPS. 2016)

 Optimizing scale-free SPVM on the Intel Xeon Phi. (Tang et al. CGO 2015)

Backgrounds & Motivation

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  • New Challenges Appear

− High Penalty when Using Greedy Grouping − Difficult to Select the Optimal Tile Size

50 100 150 200 250 300 350 soc-pokec higgs-twitter Time (second)

  • soc. blocking time
  • soc. grouping time
  • higgs. blocking time
  • higgs. grouping time
  • rig
128 256 512 1024 2048 4096 8192 16384 500 1000 1500 2000 2500 Tile Size File Size (MB) soc-pokec higgs-twitter

(a) Time Overhead (b) Memory Overhead

Backgrounds & Motivation

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Section 1 Backgrounds & Motivation

– Scale-free Graphs & Graph Algorithms – The Xeon Phi Architecture – Bucket Grouping Module – Auto-tuning Module

Section 2 The MicRun Framework Section 3 Experiments & Conclusions

Outline

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  • Overview of the Framework and the Modules

− Tiling Module − Bucket Grouping Module − Auto-tuning Module − Graph Algorithms

Workflow of the MicRun Framework.

The Mic icRun Framework

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  • Grouping Module

− Bucket Structure is introduced to construct groups − Max-heap Optimization is used to improve efficiency

1 2 3 9 4 5 6 7 8 10 11 12 13 14 15 16

  • Dest. Vertices

Source Vertices

8 7 6 5 4 3 2 1 9 1 12 6 2 10 4 13 5 14 11 7 8 3 16 15 Bucket number nnz in buckets

(a) nnz in a tile (b) nnz transformed into groups using buckets

O(n2)

Group1 Group2 Group3 Group4 Group5 Group6 SIMD Bucket 7-1-2-4 11-3-9-12 14-6-10-13 15-5-8-D 16-D-D-D NULL 16/20 Sequential

(Chen. 2016)

1-2-3-4 5-6-7-8 9-10-11-12 13-14-D-D 15-D-D-D 16-D-D-D 16/24

The Mic icRun Framework

O(n2)

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  • Grouping Module

− Bucket Structure is introduced to construct groups − Max-heap Optimization is used to improve efficiency

1 2 3 9 4 5 6 7 8 10 11 12 13 14 15 16

  • Dest. Vertices

Source Vertices

8 7 6 5 4 3 2 1 9 1 12 6 2 10 4 13 5 14 11 7 8 3 16 15 Bucket number nnz in buckets

(a) nnz in a tile (b) nnz transformed into groups using buckets

O(n2)

The Mic icRun Framework

O(n*log(b))

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  • Auto-tuning Module

− Extract Features Based on the Ideal Graph Application

 sizes of the adjust matrix of graphs is related to the sparsity character  The nnzs in the graph can influence the whole memory  The number of nnzs in each column is related to the nnzs’ distribution  The average stride between nnzs can influence the cache miss  The feature tuple is constructed as: (s, n, γ, NC , ST)

− Decision Tree Model is Employed

 The training target OT is obtained by manually probing

The Mic icRun Framework

int sum , , , 1 1 1 p q t float float c r nc g comp nc s total i j k

T T T T T nnz

  

          

  

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Section 1 Backgrounds & Motivation

– Scale-free Graphs & Graph Algorithms – The Xeon Phi Architecture – Bucket Grouping Module – Auto-tuning Module

Section 2 The MicRun Framework Section 3 Experiments & Conclusions

Outline

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  • Platform

− MIC node on the Tianhe-Ⅱ supercomputer − The version of the Xeon Phi is 31S1P − 57 X86 cores, 1.10 GHz, 4 hyper threads per core − The capacity of L2 cache is 28.5MB − Intel ICC 13.0.0, -O3 enabled

  • Graph Applications

− Bellman-Ford Algorithm − PageRank Algorithm

  • Datasets

− SNAP Dataset − University of Florida Sparse Matrix Collection

Exp xperiments

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  • College of Computer of NUDT
  • Hometown of Supercomputers: Tianhe - Ⅱ

– No. 1 in TOP500 (2013.6 – 2015.11) – 33.86 PFLOPS, 32,000 CPUs+48,000 MICs

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Experiments

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Experiments

  • Bucket Grouping vs. Seq. Grouping (Chen. 2016)

(a) Time Overhead during Grouping Stage (b) SIMD utilization by two Grouping Strategies

− Grouping Time Overhead − SIMD Utilization Ratio

Decrease stably Converge to 1 faster

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  • The Execution of two Graph Algorithms

(a) Comparison of Execution Time (b) Execution Time of Bellman-Ford (c) Execution Time of PageRank

1.2x on Average Experiments

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Datasets Bellman-Ford PageRank

  • OPT. vs. SEQ.
  • AUTO. vs. SEQ.
  • OPT. vs. SEQ.
  • AUTO. vs. SEQ.

Val Size Val Size Val Size Val Size lp_osa_60 1.08 1024 1.03 256 1.07 256 1.07 256 msdoor 1.11 1152 1.05 4096 1.14 512 1.14 512 rajat24 1.18 2048 1.09 256 1.09 768 1.09 768 Si87H76 1.05 128 1.05 128 1.14 128 1.03 512 higgs-twitter 1.26 896 1.13 3072 1.33 1024 1.21 640 kron-logn18 1.29 4096 1.29 4096 1.36 2048 1.25 1024 SPEEDUP ACHIEVED BY OPT. AND AUTO. TILING OVER SEQUENTIAL TILING PERFORMANCE

  • The Performance of the Auto-tuning Module

Optimal 0ver Sequential 1.05x ~ 1.36x Auto-tuning 0ver Sequential 1.03x ~ 1.29x

Experiments

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  • The MicRun Framework

− Grouping Module

 Bucket structure is employed  Max-heap mechanism is embedded

− Auto-tuning Module

 Decision Tree Classifier is introduced

  • Future work

− Enrich the graph algorithms built-in − Expand the framework to MIMD parallel level

Conclusions

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The Tianhe-2 supercomputer is available online. All the scientists can collaborate with us to develop new software and access Tianhe-2 through the Internet.

Welcome to contact us !

Email: linjie15@nudt.edu.cn

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Thank you! Questions？