Elsevier

Information Sciences

Volume 111, Issues 1–4, November 1998, Pages 223-237
Information Sciences

Partitioning graphs on message-passing machines by pairwise mincut

https://doi.org/10.1016/S0020-0255(98)10005-1Get rights and content

Abstract

Realizing the potential of massively parallel machines requires good solutions to the problem of mapping computations among processors so that execution is load-balanced with low inter-processor communication resulting in low execution time. This problem is typically treated as a graph partitioning problem. We develop a parallel heuristic algorithm for partitioning the vertices of a graph into many clusters so that the number of inter-cluster edges is minimized. The algorithm is designed for message-passing machines such as hypercubes. This algorithm is suitable for use with runtime approaches that have been recently developed for parallelizing unstructured scientific computations. We present a parallelization of the Kernighan-Lin heuristic that starts with an initial random multiway partition and performs pairwise improvements through application of the mincut bisection heuristic, known as Partitioning by Pairwise Mincut (PPM). A novel parallel scheme providing nearly linear speedup is developed for PPM that is optimal in terms of communication.

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1

Supported in part by an NSF Young Investigator Award CCR-9457768, by an NSF grant CCR-9210422 and by the Louisiana Board of Regents through contract LEQSF(1991-94)-RD-A-09.

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