Approximating connected facility location problems via random facility sampling and core detouring

  • Authors:

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

  • Affiliations:

  • Institut für Mathematik, Universität Paderborn, Germany;"La Sapienza" Università di Roma, Roma, Italy;Institut für Mathematik, Universität Paderborn, Germany;Institut für Mathematik, Technische Universität Berlin, Germany

  • Venue:
  • Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
  • Year:
  • 2008

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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. We show that our connected facility location algorithms 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.