A faster approximation algorithm for 2-edge-connectivity augmentation

Abstract

Given a weighted graph G with n vertices and m edges, the 2-edge-connectivity augmentation problem is that of finding a minimum weight set of edges of G to be added to a spanning subgraph H of G to make it 2-edge-connected. Such a problem is well-known to be NP-hard, but it becomes solvable in polynomial time if H is a depth-first search tree of G, and the fastest algorithm for this special case runs in O(m + nlogn) time. In this paper, we sensibly improve such a bound, by providing an efficient algorithm running in O(M · α (M,n)) time, where α is the classic inverse of the Ackermann's function and M = m · α(m,n). This algorithm has two main consequences: First, it provides a faster 2-approximation algorithm for the general 2-edge-connectivity augmentation problem; second, it solves in O(m · α (m,n)) time the problem of maintaining, by means of a minimum weight set of edges, the 2-edge-connectivity of a 2-edge-connected communication network undergoing an edge failure, thus improving the previous O(m +nlogn) time bound. © Springer-Verlag Berlin Heidelberg 2002.