Encyclopedia of Algorithms

Editors: Ming-Yang Kao

Local Search for K-medians and Facility Location

2001; Arya, Garg, Khandekar, Meyerson, Munagala, Pandit
  • Kamesh Munagala
DOI: https://doi.org/10.1007/978-0-387-30162-4_212

Keywords and Synonyms

k-Medians; k-Means; k-Medioids; Facility location; Point location; Warehouse location; Clustering     

Problem Definition

Clustering is a form of unsupervised learning, where the goal is to “learn” useful patterns in a data set \( { \mathcal{D} } \)

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Recommended Reading

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    Arya, V., Garg, N., Khandekar, R., Meyerson, A., Munagala, K., Pandit, V.: Local search heuristics for k-median and facility location problems. SIAM J. Comput. 33(3), 544–562 (2004)MathSciNetMATHGoogle Scholar
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    Charikar, M., Guha, S.: Improved combinatorial algorithms for facility location problems. SIAM J. Comput. 34(4), 803–824 (2005)MathSciNetMATHGoogle Scholar
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    Charikar, M., Guha, S., Tardos, É., Shmoys, D.B.: A constant-factor approximation algorithm for the k-median problem (extended abstract). In: STOC '99: Proceedings of the thirty-first annual ACM symposium on Theory of computing, pp. 1–10. Atlanta, May 1-4 1999Google Scholar
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    Chudak, F.A., Williamson, D.P.: Improved approximation algorithms for capacitated facility location problems. Math. Program. 102(2), 207–222 (2005)MathSciNetMATHGoogle Scholar
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    Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. J. ACM 50(6), 795–824 (2003)MathSciNetGoogle Scholar
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    Jain, K., Vazirani, V.V.: Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and lagrangian relaxation. J. ACM 48(2), 274–296 (2001)MathSciNetMATHGoogle Scholar
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    Kaufman, L., Rousseeuw, P.J.: Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York (1990)Google Scholar
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    Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic for facility location problems. In: SODA '98: Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms, pp. 1–10. San Francisco, USA; 25–26 January 1998Google Scholar
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    Kuehn, A.A., Hamburger, M.J.: A heuristic program for locating warehouses. Management Sci. 9(4), 643–666 (1963)CrossRefGoogle Scholar
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    Lin, J.-H., Vitter, J.S.: ε-approximations with minimum packing constraint violation (extended abstract). In: STOC '92: Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pp. 771–782. Victoria (1992)Google Scholar
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    Mahdian, M., Pál, M.: Universal facility location. In: European Symposium on Algorithms, pp. 409–421. Budapest, Hungary, September 16–19 2003Google Scholar
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    Ng, R.T., Han, J.: Efficient and effective clustering methods for spatial data mining. In: Proc. Symp. on Very Large Data Bases (VLDB), pp. 144–155. Santiago de Chile, 12–15 September 1994 Google Scholar
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    Pál, M., Tardos, É., Wexler, T.: Facility location with nonuniform hard capacities. In: Proceedings of the 42nd Annual Symposium on Foundations of Computer Science, pp. 329–338. Las Vegas, 14–17 October 2001Google Scholar
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    Shmoys, D.B., Tardos, É., and Aardal, K.: Approximation algorithms for facility location problems. In: Proceedings of the Twenty-Ninth Annual ACM Symposium on Theory of Computing, pp. 265–274. El Paso, 4–6 May 1997Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Kamesh Munagala
    • 1
  1. 1.Levine Science Research CenterDuke UniversityDurhamUSA