Parallel Maximum Independent Set in Convex Bipartite Graphs

A bipartite graph G = (V;W; E) is called convex if the vertices in W can be ordered in such a way that the elements of W adjacent to any vertex v 2 V form an interval (i.e. a sequence consecutively numbered vertices). Such a graph can be represented in a compact form that requires O(n) space, where n = maxfjV j; jW jg. Given a convex bipartite graph G in the compact form Dekel and Sahni designed an O(log 2 (n))-time, n-processor EREW PRAM algorithm to compute a maximum matching in G. We show that the matching produced by their algorithm can be used to construct optimally in parallel a maximum set of independent vertices. Our algorithm runs in O(log n) time with n=log n processors on a CRCW PRAM.