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A \((5.83+\epsilon )\)-Approximation Algorithm for Universal Facility Location Problem with Linear Penalties

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Combinatorial Optimization and Applications

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9486))

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Abstract

In the universal facility location problem, we are given a set of clients and facilities. Our goal is to find an assignment such that the total connection and facility cost is minimized. The connection cost is proportional to the distance between each client and its assigned facility, whereas the facility cost is a nondecreasing function with respect to the total number of clients assigned to the facility. The universal facility location problem generalizes several classical facility location problems, including the uncapacitated facility location problem and the capacitated facility location problem (both hard and soft capacities). This work considers the universal facility location problem with linear penalties, where each client can be rejected for service with a penalty. The objective is to minimize the total connection, facility and penalty cost. We present a \((5.83+\epsilon )\)-approximation local search algorithm for this problem.

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Acknowledgements

The research of the first author is supported by Collaborative Innovation Center on Beijing Society-Building and Soccial Governance. The second author’s research is supported by NSFC (Nos. 11371001 and 11531014). The third author’s research is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant 283106. The fourth author’s research is supported by NSFC (No. 11501412).

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Authors and Affiliations

  1. Department of Information and Operations Research, College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, People’s Republic of China

    Yicheng Xu & Dachuan Xu

  2. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

  3. College of Science, Tianjin University of Technology, Tianjin, 300384, People’s Republic of China

    Chenchen Wu

Authors
  1. Yicheng Xu
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  2. Dachuan Xu
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  3. Donglei Du
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  4. Chenchen Wu
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Corresponding author

Correspondence to Dachuan Xu .

Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Marywood University, Scranton, Pennsylvania, USA

    Zaixin Lu

  2. North Carolina Central University, Durham, North Carolina, USA

    Donghyun Kim

  3. University of Texas at Dallas, Richardson, Texas, USA

    Weili Wu

  4. Texas Southern University, Houston, Texas, USA

    Wei Li

  5. University of Texas at Dallas, Richardson, Texas, USA

    Ding-Zhu Du

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Xu, Y., Xu, D., Du, D., Wu, C. (2015). A \((5.83+\epsilon )\)-Approximation Algorithm for Universal Facility Location Problem with Linear Penalties. In: Lu, Z., Kim, D., Wu, W., Li, W., Du, DZ. (eds) Combinatorial Optimization and Applications. Lecture Notes in Computer Science(), vol 9486. Springer, Cham. https://doi.org/10.1007/978-3-319-26626-8_6

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  • DOI: https://doi.org/10.1007/978-3-319-26626-8_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26625-1

  • Online ISBN: 978-3-319-26626-8

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