Scalable Single Source Shortest Path Algorithms for Massively Parallel Systems

We consider the single-source shortest path (SSSP) problem: given an undirected graph with integer edge weights and a source vertex <inline-formula><tex-math notation="LaTeX">v</tex-math> <inline-graphic xlink:href="chakaravarthy-ieq1-2634535.gif"/> </i...

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Published in:IEEE transactions on parallel and distributed systems Vol. 28; no. 7; pp. 2031 - 2045
Main Authors: Chakaravarthy, Venkatesan T., Checconi, Fabio, Murali, Prakash, Petrini, Fabrizio, Sabharwal, Yogish
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Apexes
Benchmark testing
Blogs
Communications traffic
delta stepping
distributed system
graph 500 benchmark
Graph theory
Graphs
Load management
parallel algorithm
Parallel algorithms
Pruning
Shortest path
Shortest-path problems
Very large scale integration
ISSN:1045-9219, 1558-2183
Online Access:Get full text
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Summary:We consider the single-source shortest path (SSSP) problem: given an undirected graph with integer edge weights and a source vertex <inline-formula><tex-math notation="LaTeX">v</tex-math> <inline-graphic xlink:href="chakaravarthy-ieq1-2634535.gif"/> </inline-formula>, find the shortest paths from <inline-formula><tex-math notation="LaTeX">v</tex-math> <inline-graphic xlink:href="chakaravarthy-ieq2-2634535.gif"/> </inline-formula> to all other vertices. In this paper, we introduce a novel parallel algorithm, derived from the Bellman-Ford and Delta-stepping algorithms. We employ various pruning techniques, such as edge classification and direction-optimization, to dramatically reduce inter-node communication traffic, and we propose load balancing strategies to handle higher-degree vertices. These techniques are particularly effective on power-law graphs, as demonstrated by our extensive performance analysis. In the largest tested configuration, an R-MAT graph with <inline-formula><tex-math notation="LaTeX">2^{38}</tex-math> <inline-graphic xlink:href="chakaravarthy-ieq3-2634535.gif"/> </inline-formula> vertices and <inline-formula><tex-math notation="LaTeX">2^{42}</tex-math> <inline-graphic xlink:href="chakaravarthy-ieq4-2634535.gif"/> </inline-formula> edges on 32,768 Blue Gene/Q nodes, we have achieved a processing rate of three Trillion Edges Per Second (TTEPS), a four orders of magnitude improvement over the best published results.
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ISSN:1045-9219
1558-2183
DOI:10.1109/TPDS.2016.2634535