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A 7/3-Approximation for the Minimum Weight 3-Connected Spanning Subgraph Problem
Hiroshi NAGAMOCHI Katsuhiro SEKI Toshihide IBARAKI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2000/04/25
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
undirected graph, vertex-connectivity, approximation algorithm, spanning subgraph,
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We consider the problem of finding a minimum weight k-connected spanning subgraph of a given edge-weighted graph G for k=3. The problem is known to be NP-hard for k 2, and there are an O(n2m) time 3-approximation algorithm due to Nutov and Penn and an O(n8) time 2-approximation algorithm due to Dinitz and Nutov, where n and m are the numbers of vertices and edges in G, respectively. In this paper, we present a 7/3-approximation algorithm which runs in O(n2m) time.