A faster computation of the most vital edge of a shortest path
Let P-G(r, s) denote a shortest path between two nodes r and s in an undirected graph G = (V, E) such that /V/ = n and /E/ = m and with a positive real length w(e) associated with any e E E. In this paper we focus on the problem of finding an edge e* is an element of P-G(r, s) whose removal is such that the length of PG-e*(r, s) is maximum, where G - e* = (V, E \ {e*}). Such an edge is known as the most vital edge of the path P-G(r, s). We will show that this problem can be solved in O(m.alpha (m, n)) time, where ct is the functional inverse of the Ackermann function, thus improving on the previous O(m + n log n) time bound. (C) 2001 Elsevier Science B.V. All rights reserved.
most vital edge shortest path graph algorithms transient failure replacement shortest path