Minimum cost source location problems with flow requirements

  • Authors:

  • Mariko Sakashita;Kazuhisa Makino;Satoru Fujishige

  • Affiliations:

  • Graduate School of Informatics, Kyoto University, Kyoto, Japan;Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan;Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan

  • Venue:
  • LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
  • Year:
  • 2006

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Abstract

In this paper, we consider source location problems and their generalizations with three connectivity requirements λ, κ and ${\hat\kappa}$. We show that the source location problem with edge-connectivity requirement λ in undirected networks is strongly NP-hard, and that no source location problems with three connectivity requirements in undirected/directed networks are approximable within a ratio of O(ln D), unless NP has an O(NloglogN)-time deterministic algorithm. Here D denotes the sum of given demands. We also devise (1+ln D)-approximation algorithms for all the extended source location problems if we have the integral capacity and demand functions. Furthermore, we study the extended source location problems when a given graph is a tree. Our algorithms for all the extended source location problems run in pseudo-polynomial time and the ones for the source location problem with vertex-connectivity requirements κ and ${\hat\kappa}$ run in polynomial time, where pseudo-polynomiality for the source location problem with the arc-connectivity requirement λ is best possible unless P=NP, since it is known to be weakly NP-hard, even if a given graph is a tree.