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Algorithmica

, Volume 80, Issue 3, pp 1041–1072 | Cite as

Improved Approximation Algorithms for Capacitated Fault-Tolerant k-Center

  • Cristina G. Fernandes
  • Samuel P. de Paula
  • Lehilton L. C. Pedrosa
Article
  • 346 Downloads
Part of the following topical collections:
  1. Special Issue on Theoretical Informatics

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 any \(\alpha \) 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 best previously 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. We also derive approximations for the capacitated fault-tolerant k-supplier problem.

Keywords

Capacitated k-center Fault tolerance Approximation algorithm Non-uniform capacities Linear Programming LP rounding 

Notes

Acknowledgements

We would like to thank the anonymous reviewers for their careful checking of the manuscript and valuable comments.

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Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of São PauloSão PauloBrazil
  2. 2.Institute of ComputingUniversity of CampinasCampinasBrazil

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