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The Submodular Facility Location Problem and the Submodular Joint Replenishment Problem

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Approximation and Online Algorithms (WAOA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8952))

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Abstract

In this paper we consider natural generalizations of the facility location problem and the joint replenishment problem in which the opening cost of facilities and the ordering cost over the planning horizon is characterized by a submodular set function in the oracle model. Specifically, we can access the function only through a blackbox that returns the value of the function for a given set. We prove information theoretic lower bounds that these two problems cannot be approximated by any polynomial-time algorithm better than a ratio of \(O(\sqrt{n}/\log ^2{n})\). Moreover, we give \(O(\sqrt{n}\cdot \log n)\)-approximation algorithms for the two problems.

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Acknowledgments

The work was partially supported by grant NSF–CCF1115256. The author also would like to thank David Williamson for his constant help and Chaoxu Tong for inspiring discussions.

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Authors and Affiliations

  1. School of Operations Research and Information Engineering, Cornell University, Ithaca, NY, 14853, USA

    Sin-Shuen Cheung

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  1. Sin-Shuen Cheung
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Correspondence to Sin-Shuen Cheung .

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Editors and Affiliations

  1. Université Pierre et Marie Curie, LIP6, Paris, France

    Evripidis Bampis

  2. EPFL-IC, Lausanne, Switzerland

    Ola Svensson

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Cheung, SS. (2015). The Submodular Facility Location Problem and the Submodular Joint Replenishment Problem. In: Bampis, E., Svensson, O. (eds) Approximation and Online Algorithms. WAOA 2014. Lecture Notes in Computer Science(), vol 8952. Springer, Cham. https://doi.org/10.1007/978-3-319-18263-6_7

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  • DOI: https://doi.org/10.1007/978-3-319-18263-6_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18262-9

  • Online ISBN: 978-3-319-18263-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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