A Parallel Algorithm for Multilevel Graph Partitioning and Sparse Matrix Ordering

In this paper we present a parallel formulation of the multilevel graph partitioning and sparse matrix ordering algorithm. A key feature of our parallel formulation (that distinguishes it from other proposed parallel formulations of multilevel algorithms) is that it partitions the vertices of the gr...

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Bibliographic Details
Published in:Journal of parallel and distributed computing Vol. 48; no. 1; pp. 71 - 95
Main Authors: Karypis, George, Kumar, Vipin
Format: Journal Article
Language:English
Published: San Diego, CA Elsevier Inc 10.01.1998
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Exact sciences and technology
fill reducing ordering
Information retrieval. Graph
multilevel partitioning methods
numerical linear algebra
parallel graph partitioning
Software
Theoretical computing
numerical linear algebra
parallel graph partitioning
fill reducing ordering
multilevel partitioning methods
Partition
Parallel algorithm
Distributed memory multiprocessor system
Numerical computation
Algorithm performance
Linear algebra
Sparse matrix
Graph theory
Distributed system
Experimental study
ISSN:0743-7315, 1096-0848
Online Access:Get full text
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Summary:In this paper we present a parallel formulation of the multilevel graph partitioning and sparse matrix ordering algorithm. A key feature of our parallel formulation (that distinguishes it from other proposed parallel formulations of multilevel algorithms) is that it partitions the vertices of the graph intopparts while distributing the overall adjacency matrix of the graph among allpprocessors. This mapping results in substantially smaller communication than one-dimensional distribution for graphs with relatively high degree, especially if the graph is randomly distributed among the processors. We also present a parallel algorithm for computing a minimal cover of a bipartite graph which is a key operation for obtaining a small vertex separator that is useful for computing the fill reducing ordering of sparse matrices. Our parallel algorithm achieves a speedup of up to 56 on 128 processors for moderate size problems, further reducing the already moderate serial run time of multilevel schemes. Furthermore, the quality of the produced partitions and orderings are comparable to those produced by the serial multilevel algorithm that has been shown to outperform both spectral partitioning and multiple minimum degree.
ISSN:0743-7315
1096-0848
DOI:10.1006/jpdc.1997.1403