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 + n log n) time. In this paper, we sensibly improve such a bound, by providing an efficient algorithm running in O(M ? ?(M, n)) time, where ? is the classic inverse of the Ackermann's function and M = m ? ?(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 ? ?(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 + n log n) time bound.
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