Parallel algorithm for finding the most vital edge in weighted graphs

Let G = (V, E) be a weighted undirected graph with n vertices and m edges; each edge e has a weight w(e) assigned to it. Let f(G) be the weight of a minimum spanning tree of G if G is connected; otherwise f(G) = infinity. The most vital edge of G is an edge e such that f(G - e) greater than or equal to f(G - e') for every other edge e' of G, In this paper we describe an O(log n) time parallel algorithm with in processors for finding the most vital edge of a graph on the concurrent read exclusive write (CREW) model of parallel computation. (C) 1997 Academic Press.