An approximation for finding a smallest 2-edge-connected subgraph containing a specifed spanning tree

Authors:
Hiroshi Nagamochi;Toshihide Ibaraki
Affiliations:
Kyoto University, Kyoto, Japan;Kyoto University, Kyoto, Japan
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

Given a graph G = (V, E) and a tree T = (V, F) with E ∩ F = θ such that G + T = (V, F ∪ E) is 2-edge-connected, we consider the problem of finding a smallest 2-edge-connected spanning subgraph (V, F ∪ E′) of G + T containing T. The problem, which is known to be NP-hard, admits a 2-approximation algorithm. However, obtaining a factor better than 2 for this problem has been one of the main open problems in the graph augmentation problem. In this paper, we present an O(√nm) time 12/7 -approximation algorithm for this problem, where n = |V| and m = |E ∪ F|