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An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem

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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX 2007, RANDOM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4627))

Abstract

We consider the metric uncapacitated facility location problem(UFL). In this paper we modify the (1 + 2/e)-approximation algorithm of Chudak and Shmoys to obtain a new (1.6774,1.3738)- approximation algorithm for the UFL problem. Our linear programing rounding algorithm is the first one that touches the approximability limit curve \((\gamma_f, 1+2e^{-\gamma_f})\) established by Jain et al. As a consequence, we obtain the first optimal approximation algorithm for instances dominated by connection costs.

Our new algorithm - when combined with a (1.11,1.7764)-approxima- tion algorithm proposed by Jain, Mahdian and Saberi, and later analyzed by Mahdian, Ye and Zhang - gives a 1.5-approximation algorithm for the metric UFL problem. This algorithm improves over the previously best known 1.52-approximation algorithm by Mahdian, Ye and Zhang, and it cuts the gap with the approximability lower bound by 1/3.

The algorithm is also used to improve the approximation ratio for the 3-level version of the problem.

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Author information

Authors and Affiliations

  1. Centrum voor Wiskunde en Informatica, Kruislaan 413, NL-1098 SJ Amsterdam, Netherlands

    Jaroslaw Byrka

Authors
  1. Jaroslaw Byrka
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Editor information

Editors and Affiliations

  1. Computer Science Dept., Princeton University, 35 Olden Street, NJ 08540-5233, Princeton, USA

    Moses Charikar

  2. Institut für Informatik, Christian-Albrechts-Universität zu Kiel,, Olshausenstr. 40, 24098, Kiel, Germany

    Klaus Jansen

  3. Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, 76100, Rehovot, Israel

    Omer Reingold

  4. Centre Universitaire d’Informatique,, Battelle bâtiment A, route de Drize 7, 1227, Geneva, Carouge, Switzerland

    José D. P. Rolim

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Byrka, J. (2007). An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. APPROX RANDOM 2007 2007. Lecture Notes in Computer Science, vol 4627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74208-1_3

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  • DOI: https://doi.org/10.1007/978-3-540-74208-1_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74207-4

  • Online ISBN: 978-3-540-74208-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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