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(nkα((k+1)(n−1),n)), which improves a previously known result by an O(n/α((k+1)(n−1),n)) factor, where α is a functional inverse of Ackermannʹs function which grows very slow. The parallel version of the algorithm takes O(log n log log n) time using O(nk/log n) processors on a CREW PRAM.