Minimum cost source location problem with local 3-vertex-connectivity requirements

  • Authors:

  • Toshimasa Ishii;Hitoshi Fujita;Hiroshi Nagamochi

  • Affiliations:

  • Toyohashi University of Technology, Aichi, Japan;Matsushita Systems and Technology Co., Ltd., Osaka, Japan;Kyoto University, Kyoto, Japan

  • Venue:
  • CATS '05 Proceedings of the 2005 Australasian symposium on Theory of computing - Volume 41
  • Year:
  • 2005

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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 ε V has a demand d(ν) ε Z+ and a cost c(ν) ε R+, where Z+ and R+ denote the set of nonnegative integers and the set of nonnegative reals, respectively. The source location problem with vertex-connectivity requirements in a given graph G asks to find a set S of vertices minimizing ΣνεS c(ν) such that there are at least d(ν) pairwise vertex-disjoint paths from S to ν for each vertex ν ε V - S. It is known that if there exists a vertex ν ε V with d(ν) ≥ 4, then the problem is NP-hard even in the case where every vertex has a uniform cost. In this paper, we show that the problem can be solved in O(|V|4(log|V|)2) time if d(ν) ≤ 3 holds for each vertex v ε V.