LACC: A Linear-Algebraic Algorithm for Finding Connected Components in Distributed Memory

Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computat...

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Bibliographic Details
Published in:Proceedings - IEEE International Parallel and Distributed Processing Symposium pp. 2 - 12
Main Authors: Azad, Ariful, Buluc, Aydin
Format: Conference Proceeding
Language:English
Published: IEEE 01.05.2019
Subjects:
Clustering algorithms
Computational modeling
connected components
Forestry
graph algorithm
GraphBLAS
parallel algorithm
Partitioning algorithms
Phase change random access memory
Sparse matrices
Vegetation
ISSN:1530-2075
Online Access:Get full text
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Summary:Finding connected components is one of the most widely used operations on a graph. Optimal serial algorithms for the problem have been known for half a century, and many competing parallel algorithms have been proposed over the last several decades under various different models of parallel computation. This paper presents a parallel connected-components algorithm that can run on distributed-memory computers. Our algorithm uses linear algebraic primitives and is based on a PRAM algorithm by Awerbuch and Shiloach. We show that the resulting algorithm, named LACC for Linear Algebraic Connected Components, outperforms competitors by a factor of up to 12× for small to medium scale graphs. For large graphs with more than 50B edges, LACC scales to 4K nodes (262K cores) of a Cray XC40 supercomputer and outperforms previous algorithms by a significant margin. This remarkable performance is accomplished by (1) exploiting sparsity that was not present in the original PRAM algorithm formulation, (2) using high-performance primitives of Combinatorial BLAS, and (3) identifying hot spots and optimizing them away by exploiting algorithmic insights.
ISSN:1530-2075
DOI:10.1109/IPDPS.2019.00012