A Fast and Simple Randomized Parallel Algorithm for Maximal Matching

Let G(V, E) be an undirected graph. A set M ~ E is a matching if no two edges of M have a common vertex. The matching M is maximal if it is not properly contained in any other matching. Note that this does not necessarily imply that M has more edges than any other matching. A maximal matching can be found sequentially by the following greedy algorithm: Start with an empty matching and add any edge which is not adjacent to any edge that i sa l ready in M. Unfortunately, it is not clear how to use parallelism to implement this algorithm in less than linear time. The best known deterministic parallel algorithm for maximal matching is given in [2], where I V I + I E I processors are needed to find a maximal matching of a graph G(V, E) in log 3 I EI time. The model of computat ion is the CRCW-PRAM which allows simultaneous READ/WRITE by more