Finding the k Most Vital Edges with Respect to Minimum Spanning Trees for k=2 and 3

Let G(V, E) be a weighted, undirected, connected simple graph with n vertices and m edges. The k most vital edge problem with respect to minimum spanning trees is to find a set S of k edges from E such that the removal of all edges in S results in the greatest increase in the weight of the minimum spanning tree in the remaining graph G(V, E - S ). In this paper we present a better algorithm to solve this problem for k = 2 and 3. The proposed algorithms run in times O(n2 (3n, n)) for k = 2 and O(n3 (4n, n)) for k = 3, which improve previously known results by O(n/(3n, n)) and O(n/(4n, n)) factors, respectively, where is a functional inverse of Ackermann's function. The algorithms can also be implemented on a CREW PRAM in which case they need O(log n log log n) time using O(m + n2 / log n) processors, and O(log n log log n) time using O(n3 / log n) processors, respectively.

• Type: Conference
• Year: 1998
• Where: CATS
• Authors: Weifa Liang, George Havas
• Keywords: CATS 1998, CATS 2007, Minimum Spanning Tree, Simple Graph, Vital Edge Problem