Connected facility location via random facility sampling and core detouring

  • Authors:

  • Friedrich Eisenbrand;Fabrizio Grandoni;Thomas Rothvoí;Guido Schäfer

  • Affiliations:

  • Institute of Mathematics, ícole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland;Dipartimento di Informatica, Sistemi e Produzione, Universití di Roma Tor Vergata, Via del Politecnico 1, 00133 Roma, Italy;Institute of Mathematics, ícole Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland;Centrum Wiskunde & Informatica, PO Box 94079, 1090 GB Amsterdam, The Netherlands

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2010

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Abstract

We present a simple randomized algorithmic framework for connected facility location problems. The basic idea is as follows: We run a black-box approximation algorithm for the unconnected facility location problem, randomly sample the clients, and open the facilities serving sampled clients in the approximate solution. Via a novel analytical tool, which we term core detouring, we show that this approach significantly improves over the previously best known approximation ratios for several NP-hard network design problems. For example, we reduce the approximation ratio for the connected facility location problem from 8.55 to 4.00 and for the single-sink rent-or-buy problem from 3.55 to 2.92. The mentioned results can be derandomized at the expense of a slightly worse approximation ratio. The versatility of our framework is demonstrated by devising improved approximation algorithms also for other related problems.