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Listing Cliques in Parallel Using a Beowulf Cluster

Although there are efficient algorithms for many problems in graph theory, there remain intractable problems that require time exponential in the number of vertices. Fortunately, many of these algorithms can be implemented in parallel to reduce the run-time. The emergence of the Beowulf Cluster (the poor man’s supercomputer) and more recently, multicore desktop processors has enabled small institutions, labs and even individuals to solve larger instances of these problems within reasonable time lines. In this paper we test a parallel implementation of a modified version of the Bron-Kerbosch Algorithm for listing the maximal cliques of a graph. We outline the benefits of parallelism, demonstrate some of the software tools available, and discuss problems we encountered.