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Facility Location on Planar Graphs with Unreliable Links

  • N. S. Narayanaswamy
  • Meghana Nasre
  • R. Vijayaragunathan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10846)

Abstract

Hassin et al. [9] consider the Max-Exp-Cover-R problem to study the facility location problem on a graph in the presence of unreliable links when the link failure is according to the Linear Reliability Order (LRO) model. They showed that for unbounded R the problem is polynomial time solvable and for \(R=1\) and planar graphs the problem is NP-Complete. In this paper, we study the Max-Exp-Cover-1 problem under the LRO edge failure model. We obtain a fixed parameter tractable algorithm for Max-Exp-Cover-1 problem for bounded treewidth graphs, parameterized by the treewidth. We extend the Baker’s technique (Baker, J. ACM 1994) to obtain PTAS for Max-Exp-Cover-1 problem under the LRO model on planar graphs. We observe that the coverage function of the Max-Exp-Cover-R problem is submodular and the problem admits a \((1-1/e)\)-approximation for any failure model in which the expected coverage of a set by another set can be computed in polynomial time.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • N. S. Narayanaswamy
    • 1
  • Meghana Nasre
    • 1
  • R. Vijayaragunathan
    • 1
  1. 1.Department of Computer Science and EngineeringIndian Institute of Technology MadrasChennaiIndia

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