The source location problem with local 3-vertex-connectivity requirements

Authors:
Toshimasa Ishii;Hitoshi Fujita;Hiroshi Nagamochi
Affiliations:
Department of Information and Management Science, Otaru University of Commerce, Otaru, Hokkdaido 047-8501, Japan;Matsushita Systems and Technology Co. Ltd., Osaka 540-6321, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

Let G=(V,E) be a simple undirected graph with a set V of vertices and a set E of edges. Each vertex v@?V has an integer valued demand d(v)=0. The source location problem with vertex-connectivity requirements in a given graph G asks to find a set S of vertices with the minimum cardinality such that there are at least d(v) vertex-disjoint paths between S and each vertex v@?V-S. In this paper, we show that the problem with d(v)==4 for some vertex v@?V, the problem is NP-hard.