FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
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Given a graph G of n vertices and m edges, and given a spanning subgraph H of G, the problem of finding a minimum weight set of edges of G, denoted as Aug2(H,G), to be added to H to make it 2-edge connected, is known to be NP-hard. In this paper, we present polynomial time effcient algorithms for solving the special case of this classic augmentation problem in which the subgraph H is a Hamiltonian path of G. More precisely, we show that if G is unweighted, then Aug2(H,G) can be computed in O(m) time and space, while if G is non-negatively weighted, then Aug2(H,G) can be comp uted in O(m+n log n) time and O(m) space. These results have an interesting application for solving a survivability problem on communication networks.