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A constant-factor approximation algorithm for the k-median problem (extended abstract)

Authors:

Moses Charikar,

Sudipto Guha,

�va Tardos,

David B. ShmoysAuthors Info & Claims

STOC '99: Proceedings of the thirty-first annual ACM symposium on Theory of Computing

Pages 1 - 10

https://doi.org/10.1145/301250.301257

Published: 01 May 1999 Publication History

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References

[1]

S. Arora, P. Raghavan and S. Rao. Approximation schemes for Euclidean k-medians and related problems. Proceedings of the 30th Annual A CM Symposium on Theory of Computing, pp. 106-113, 1998.]]

Digital Library

Google Scholar

[2]

J. Bar-Ilan, G. Kortsarz, and D. Peleg. How to allocate network centers. J. Algorithms, 15:385- 415, 1993.]]

Digital Library

Google Scholar

[3]

Y. Bartal. Probabilistic approximation of metric spaces and its algorithmic applications. In Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science, pages 184-193, 1996.]]

Digital Library

Google Scholar

[4]

Y. Baxtal. On approximating arbitrary metrics by tree metrics. In Proceedings of the 30th Annual A CM Symposium on Theory of Computing, pages 161-168, 1998.]]

Digital Library

Google Scholar

[5]

M. Charikar, C. Chekuri, A. Goel, and S. Guha. Rounding via trees: deterministic approximation algorithms for group Steiner crees and k-median. In Proceedings of the $Oth Annual A CM Symposium on Theory of Computing, pages 114-123, 1998.]]

Digital Library

Google Scholar

[6]

F. A. Chudak. Improved approximation algorithms for uncapacitated facility location. In R. E. Bixby, E. A. Boyd, and R. Z. Rfos-Mercado, editors, Integer Programming and Combinatorial Optimization, volume 1412 of Lecture Notes in Computer Science, pages 180-194, Berlin, 1998. Springer.]]

Google Scholar

[7]

F. Chudak and D. Shmoys. Improved approximation algorithms for the uncapacitated facility location problem. Unpublished manuscript, 1998.]]

Google Scholar

[8]

F. A. Chudak and 'D. B. Shmoys. Improved approximation algorithms for the capacitaterl facility location problem. In Proceedings of the l Oth Annual A CM-SIAM Symposium on Discrete Algorithms, pages $875-S876, t999.]]

Digital Library

Google Scholar

[9]

G. Cornu~jols, G. L. Nemhauser, and L. A. Wolsey. The uncapacitated facility location problem. In P. Mirchandani and R. Francis, editors, Discrete Location Theory, pages 119- I71. John WiIey and Sons, Inc., New York, 1990.]]

Google Scholar

[10]

M. E. Dyer and A. M. Frieze. A simple heuristic for the p-center problem. Oper. Res. Lett., 3:285-288, 1985.]]

Digital Library

Google Scholar

[11]

T. F. Gonzalez. Clustering to minimize the maximum intercluster distance. Theoret. Comput. $ci., 38:293-306, 1985.]]

Google Scholar

[12]

S. Guha and S. Khuller. Greedy strikes back: Improved facility location algorithms. In Proceedings of the 9th Ar~nual A CM-SIAM Symposium on Discrete Algorithms, pages 649-657, 1998.]]

Digital Library

Google Scholar

[13]

D. S. Hochbaum and D. B. Shmoys. A best possible approximation algorithm for the k-center problem. Math. Oper. Res., 10:180-184, 1985.]]

Digital Library

Google Scholar

[14]

O. Kariv and S. L. Hakimi. An algorithmic approach to network location problems, Part II: pmedians. SIAM J. Appl. Math., 37:539-560, 1979.]]

Crossref

Google Scholar

[15]

S. Khuller and Y. J. Sussmann. The capacitated k-center problem. In Proceedings ol~ the,~th Annual European Symposium on Algorithms, Lecture Notes in Computer Science 1136, pages 152-166, Berlin, 1996. Springer.]]

Digital Library

Google Scholar

[16]

M. R. Korupolu, C. G. Ptaxton, and R. Rajaraman. Analysis of a local search heuristic for facility location problems, in Proceedings of the 9th Annual A CM-$IAM Symposium on Discrete Algorithms, pages 1-10, 1998.]]

Digital Library

Google Scholar

[17]

J.-H. Lin and J. S. Vitter. Approximation algorithms for geometric median problems. Inform. Proc. Lett., 44:245-249, 1992.]]

Digital Library

Google Scholar

[18]

J.-H. Lin and J. S. Vitter. ~-approximations with minimum packing constraint violation. In Proceedings of the 24fth Armual A CM Symposium on Thecry of Computing, pages 771-782, 1992.]]

Digital Library

Google Scholar

[19]

D. B. Shmoys and E. Tardos. An Approximation Algorithm for the Generalized Assignment Problem. Math. Programming, 62:461-474, 1993.]]

Digital Library

Google Scholar

[20]

D. B. Shmoys, I~. Tardos, and K. I. Aardal. Approximation algorithms for facility location problems. In Proceedings ojr the 29th Annual A CM Symposium on Theory of Computing, pages 265-274, 1997.]]

Digital Library

Google Scholar

[21]

M. Sviridenko. Personal communication, July, 1998.]]

Google Scholar

[22]

A. Tamir. An O(/m2) algorithm for the p-median and related problems on tree graphs. Oper. Res. Lett., 19:59-94, 1996.]]

Digital Library

Google Scholar

[23]

S. de Vries, M. Posner, and R. Vohra. The K- median Problem on a Tree. Working paper, Ohio State University, Oct. 1998.]]

Google Scholar

[24]

J. Ward, R. T. Wong, P. Lemke, and A. Oudjit. Properties of the tree K-median linear programming relaxation. Unpublished manuscript, 1994.]]

Google Scholar

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Makarychev KShan LOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)Random cuts are optimal for explainable k-mediansProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3669043(66890-66901)Online publication date: 10-Dec-2023
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Index Terms

A constant-factor approximation algorithm for the k-median problem (extended abstract)
1. Mathematics of computing
  1. Mathematical analysis
    1. Functional analysis
      1. Approximation
  2. Probability and statistics
2. Theory of computation
  1. Design and analysis of algorithms
    1. Approximation algorithms analysis

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STOC '99: Proceedings of the thirty-first annual ACM symposium on Theory of Computing

May 1999

790 pages

ISBN:1581130678

DOI:10.1145/301250

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Published: 01 May 1999

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