Abstract

We describe a new parallel algorithm for computing a maximal matching in a graph. The algorithm runs in time O(log 4 n) on (m + n) log 4 n EREW PRAM processors. A variant of this algorithm computes a maximal matching in bipartite graphs in time O(log 3 n) on (m + n) log 3 n EREW PRAM processors. This is the first deterministic algorithm for maximal matching that achieves a linear time-processor product. We also prove a general result linking the parallel complexity of maximal matching on bipartite graphs and general graphs.

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