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Maximum-cover source location problems with objective edge-connectivity three

Author

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  • Kenya Sugihara
  • Hiro Ito

Abstract

Given a graph G=(V, E), a set of vertices $${S \subseteq V}$$ covers a vertex $${v \in V}$$ if the edge-connectivity between S and v is at least a given number k. Vertices in S are called sources. The maximum-cover source location problem, which is a variation of the source location problem, is to find a source set S with a given size at most p, maximizing the sum of the weight of vertices covered by S. In this paper, we show a polynomial-time algorithm for this problem in the case of k = 3 for a given undirected graph with a vertex weight function and an edge capacity function. Moreover, we show that this problem is NP-hard even if vertex weights and edge capacities are both uniform for general k. Copyright Springer-Verlag 2009

Suggested Citation

  • Kenya Sugihara & Hiro Ito, 2009. "Maximum-cover source location problems with objective edge-connectivity three," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(1), pages 183-193, August.
    • Handle: RePEc:spr:mathme:v:70:y:2009:i:1:p:183-193
    DOI: 10.1007/s00186-008-0266-1
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    Cited by:

    1. Lara Turner & Dwi Groß & Horst Hamacher & Sven Krumke, 2015. "Static and dynamic source locations in undirected networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 619-646, October.

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