Parallel greedy graph matching using an edge partitioning approach

We present a parallel version of the Karp-Sipser graph matching heuristic for the maximum cardinality problem. It is bulk-synchronous, separating computation and communication, and uses an edge-based partitioning of the graph, translated from a two-dimensional partitioning of the corresponding adjacency matrix. It is shown that the communication volume of Karp-Sipser graph matching is proportional to that of parallel sparse matrix-vector multiplication (SpMV), so that efficient partitioners developed for SpMV can be used. The algorithm is presented using a small basic set of 7 message types, which are discussed in detail. Experimental results show that for most matrices, edge-based partitioning is superior to vertex-based partitioning, in terms of both parallel speedup and matching quality. Good speedups are obtained on up to 64 processors.

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