A parallel algorithm for connected components on distributed memory machines

Abstract

Finding connected components (CC) of an undirected graph is a fundamental computational problem. Various CC algorithms exist for PRAM models. An implementation of a PRAM CC algorithm on a coarse-grain MIMD machine with distributed memory brings many problems, since the communication overhead is substantial compared to the local computation. Several implementations of CC algorithms on distributed memory machines have been described in the literature, all in Split-C. We have designed and implemented a CC algorithm in C++ and MPI, by combining the ideas of the previous PRAM and distributed memory algorithms. Our main optimization is based on replacing the conditional hooking by rules for reducing nontrivial cycles during the contraction of components. We have also implemented a method for reducing the number of exchanged messages which is based on buffering messages and on deferred processing of answers.