Finding the k most vital edges with respect to minimum spanning trees for fixed k
Assume that G(V,E) is a weighted, undirected, connected graph with n vertices. The k most vital edge problem with respect to a minimum spanning tree is to find a set S? of k edges from E such that the removal of the edges in S? results in the greatest increase in the weight of the minimum spanning tree in the resulting graph G(V,E?S?) . In this paper, an improved algorithm for the problem with fixed k, k?2, has been presented. The proposed algorithm runs in time O(nk?((k+1)(n?1),n)), which improves a previously known result by an O(n/?((k+1)(n?1),n)) factor, where ? is a functional inverse of Ackermann's function which grows very slow. The parallel version of the algorithm takes time using processors on a CREW PRAM.
most vital edges minimum spanning trees combinatorial algorithms network optimization parallel algorithms