PARALLEL ALGORITHMS FOR FINDING THE MOST VITAL EDGE WITH RESPECT TO MINIMUM SPANNING TREE

Abstract

Given a weighted graph G, the weight of a spanning tree T, denoted by w(T), is defined as the total weight of all edges in T. A spanning tree T in G is called a minimum spanning tree if w(T) less-than-or-equal-to w(T') for all spanning trees T' in G. Let w(G) denote the weight of the minimum spanning tree of G if G is connected; otherwise, w(G) = infinity. An edge e is called a most vital edge in G if w(G - e) greater-than-or-equal-to w(G - e') for every edge e' of G where G - e' denotes the partial graph obtained by removing e' from G. In this paper, we present several cost-optimal parallel algorithms, under different computation models, to find the most vital edge in a weighted graph.