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The Multi-service Location Problems

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New Trends in Computer Technologies and Applications (ICS 2018)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1013))

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Abstract

In this paper, we aim to provide a general study on the framework of Multi-Service Location Problems from a broader perspective and provide systematic methodologies for this category of problems to obtain approximate solutions. In this category of problems, we are to decide the location of a fixed number of facilities providing different types of services, so as to optimize certain distance measures of interest regarding how well the clients are served.

Specifically, we are to provide p types of services by locating \(k \ge p\) facilities. Each client has a demanding list for the p types of services, and evaluates its service quality by its service distance, defined as its total transportation cost to those facilities offering the demanded services. Under this framework, we address two kinds of distance measures, the maximum service distance and the average service distance of all clients, and define the p-service k-center problem and the p-service k-median problem, according to the minimax and the minisum criteria, respectively. We develop a general approach for multi-service location problems, and propose a (2p)-approximation and a 4-approximation to the two problems, respectively.

Research supported by Ministry of Science and Technology of Taiwan under Grants No. MOST 106-2221-E-001-006-MY3.

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References

  1. Ahmadian, S., Norouzi-Fard, A., Svensson, O., Ward, J.: Better guarantees for \(k\)-means and Euclidean \(k\)-median by primal-dual algorithms. In: 2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS), pp. 61–72 (2017)

    Google Scholar 

  2. Anzai, T., Ito, T., Suziki, A., Zhou, X.: The multi-service center decision problem is NP-complete for split graphs. In: Proceedings of the 6th World Congress on Engineering and Technology, CET 2016 (2016)

    Google Scholar 

  3. Byrka, J., Pensyl, T., Rybicki, B., Srinivasan, A., Trinh, K.: An improved approximation for \(k\)-median and positive correlation in budgeted optimization. ACM Trans. Algorithms 13(2), 23:1–23:31 (2017)

    Article  MathSciNet  Google Scholar 

  4. Charikar, M., Guha, S.: Improved combinatorial algorithms for the facility location and \(k\)-median problems. In: 40th Annual Symposium on Foundations of Computer Science, pp. 378–388 (1999)

    Google Scholar 

  5. Feder, T., Greene, D.: Optimal algorithms for approximate clustering. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 434–444. ACM, New York (1988)

    Google Scholar 

  6. Hochbaum, D.S., Shmoys, D.B.: A best possible heuristic for the \(k\)-center problem. Math. Oper. Res. 10(2), 180–184 (1985)

    Article  MathSciNet  Google Scholar 

  7. Ito, T., Kakimura, N., Kobayashi, Y.: Complexity of the multi-service center problem. In: Okamoto, Y., Tokuyama, T. (eds.) 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), vol. 92, pp. 48:1–48:12. Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, Dagstuhl (2017)

    Google Scholar 

  8. Jain, K., Mahdian, M., Saberi, A.: A new greedy approach for facility location problems. In: Proceedings of the Thiry-fourth Annual ACM Symposium on Theory of Computing, STOC 2002, pp. 731–740. ACM, New York (2002)

    Google Scholar 

  9. Kariv, O., Hakimi, S.L.: An algorithmic approach to network location problems. I: The \(p\)-centers. SIAM J. Appl. Math. 37(3), 513–538 (1979)

    Article  MathSciNet  Google Scholar 

  10. Kariv, O., Hakimi, S.L.: An algorithmic approach to network location problems. II: The \(p\)-medians. SIAM J. Appl. Math. 37(3), 539–560 (1979)

    Article  MathSciNet  Google Scholar 

  11. Kumar, A., Sabharwal, Y., Sen, S.: Linear-time approximation schemes for clustering problems in any dimensions. J. ACM 57(2), 5:1–5:32 (2010)

    Article  MathSciNet  Google Scholar 

  12. Megiddo, N., Supowit, K.J.: On the complexity of some common geometric location problems. SIAM J. Comput. 13(1), 182–196 (1984)

    Article  MathSciNet  Google Scholar 

  13. Plesník, J.: A heuristic for the \(p\)-center problems in graphs. Discrete Appl. Math. 17(3), 263–268 (1987)

    Article  MathSciNet  Google Scholar 

  14. Tamir, A.: An \({O}(pn^2)\) algorithm for the \(p\)-median and related problems on tree graphs. Oper. Res. Lett. 19(2), 59–64 (1996)

    Article  MathSciNet  Google Scholar 

  15. Yu, H.-I., Li, C.-C.: The multi-service center problem. In: Chao, K.-M., Hsu, T., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 578–587. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-35261-4_60

    Chapter  Google Scholar 

  16. Yu, H.I., Li, C.C., Lee, D.: The multi-service center problem. Theor. Comput. Sci. 705, 58–74 (2018)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute of Information Science, Academia Sinica, Nankang, Taipei, 115, Taiwan

    Hung-I Yu & D. T. Lee

  2. Institute of Computer Science and Information Engineering, National Chung-Cheng University, Chiayi, 621, Taiwan

    Mong-Jen Kao

Authors
  1. Hung-I Yu
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  2. Mong-Jen Kao
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  3. D. T. Lee
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Correspondence to Hung-I Yu .

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Editors and Affiliations

  1. National Yunlin University of Science and Technology, Douliu, Taiwan

    Chuan-Yu Chang

  2. National Yunlin University of Science and Technology, Douliu, Taiwan

    Chien-Chou Lin

  3. Southern Taiwan University of Science and Technology, Tainan, Taiwan

    Horng-Horng Lin

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Yu, HI., Kao, MJ., Lee, D.T. (2019). The Multi-service Location Problems. In: Chang, CY., Lin, CC., Lin, HH. (eds) New Trends in Computer Technologies and Applications. ICS 2018. Communications in Computer and Information Science, vol 1013. Springer, Singapore. https://doi.org/10.1007/978-981-13-9190-3_56

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  • DOI: https://doi.org/10.1007/978-981-13-9190-3_56

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-9189-7

  • Online ISBN: 978-981-13-9190-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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