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Improved Approximation Algorithms for Capacitated Fault-Tolerant k-Center

  • Cristina G. Fernandes
  • Samuel P. de Paula
  • Lehilton L. C. PedrosaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9644)

Abstract

In the k-center problem, given a metric space V and a positive integer k, one wants to select k elements (centers) of V and an assignment from V to centers, minimizing the maximum distance between an element of V and its assigned center. One of the most general variants is the capacitated \(\alpha \) -fault-tolerant k -center, where centers have a limit on the number of assigned elements, and, if \(\alpha \) centers fail, there is a reassignment from V to non-faulty centers. In this paper, we present a new approach to tackle fault tolerance, by selecting and pre-opening a set of backup centers, then solving the obtained residual instance. For the \(\{0,L\}\)-capacitated case, we give approximations with factor 6 for the basic problem, and 7 for the so called conservative variant, when only clients whose centers failed may be reassigned. Our algorithms improve on the previously best known factors of 9 and 17, respectively. Moreover, we consider the case with general capacities. Assuming \(\alpha \) is constant, our method leads to the first approximations for this case.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Cristina G. Fernandes
    • 1
  • Samuel P. de Paula
    • 1
  • Lehilton L. C. Pedrosa
    • 2
    Email author
  1. 1.Department of Computer ScienceUniversity of São PauloSão PauloBrazil
  2. 2.Institute of ComputingUniversity of CampinasCampinasBrazil

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