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Complexity of Single-Swap Heuristics for Metric Facility Location and Related Problems

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Algorithms and Complexity (CIAC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10236))

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Abstract

Metric facility location and K-means are well-known problems of combinatorial optimization. Both admit a fairly simple heuristic called single-swap, which adds, drops or swaps open facilities until it reaches a local optimum. For both problems, it is known that this algorithm produces a solution that is at most a constant factor worse than the respective global optimum. In this paper, we show that single-swap applied to the weighted metric uncapacitated facility location and weighted discrete K-means problem is tightly PLS-complete and hence has exponential worst-case running time.

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Acknowledgments

The author would like to thank Johannes Blömer, Jakob Juhnke and the anonymous reviewers for helpful comments which increased the quality of the paper, and Alexander Skopalik for bringing PLS to his attention.

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Authors and Affiliations

  1. Department of Computer Science, Paderborn University, Paderborn, Germany

    Sascha Brauer

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  1. Sascha Brauer
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Correspondence to Sascha Brauer .

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Editors and Affiliations

  1. National Technical University of Athens, Zografou, Athens, Greece

    Dimitris Fotakis

  2. National Technical University of Athens, Zografou, Athens, Greece

    Aris Pagourtzis

  3. Université Paris-Dauphine, Paris, France

    Vangelis Th. Paschos

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Brauer, S. (2017). Complexity of Single-Swap Heuristics for Metric Facility Location and Related Problems. In: Fotakis, D., Pagourtzis, A., Paschos, V. (eds) Algorithms and Complexity. CIAC 2017. Lecture Notes in Computer Science(), vol 10236. Springer, Cham. https://doi.org/10.1007/978-3-319-57586-5_11

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  • DOI: https://doi.org/10.1007/978-3-319-57586-5_11

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  • Print ISBN: 978-3-319-57585-8

  • Online ISBN: 978-3-319-57586-5

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