Parallel maximum independent set in convex bipartite graphs

Abstract

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 υ ϵ 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 $\text{n = max{¦V¦, ¦W¦}}$. Given a convex bipartite graph G in the compact form Dekel and Sahni designed an O(log²(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(logn) time with $\text{n}\text{logn}$ processors on an Arbitrary CRCW PRAM.