Improved Approximation Algorithms for Capacitated Facility Location Problems
 Fabián A. Chudak,
 David P. Williamson
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Abstract
In a recent surprising result, Korupolu, Plaxton, and Rajaraman [10,11] showed that a simple local search heuristic for the capacitated facility location problem (CFLP) in which the service costs obey the triangle inequality produces a solution in polynomial time which is within a factor of 8 + ε of the value of an optimal solution. By simplifying their analysis, we are able to show that the same heuristic produces a solution which is within a factor of 6(1 + ε) of the value of an optimal solution. Our simplified analysis uses the supermodularity of the cost function of the problem and the integrality of the transshipment polyhedron.
Additionally, we consider the variant of the CFLP in which one may open multiple copies of any facility. Using ideas from the analysis of the local search heuristic, we show how to turn any αapproximation algorithm for this variant into one which, at an additional cost of twice the optimum of the standard CFLP, opens at most one additional copy of any facility. This allows us to transform a recent 3approximation algorithm of Chudak and Shmoys [5] that opens many additional copies of facilities into a polynomialtime algorithm which only opens one additional copy and has cost no more than five times the value of the standard CFLP.
 S. Arora and M. Sudan. Improved lowdegree testing and its applications. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 4850–495, 1997.
 Dj. A. Babayev. Comments on the note of Frieze. Mathematical Programming 7:249–252, 1974. CrossRef
 F. Barahona and D. Jensen. Plant location with minimum inventory. Mathematical Programming 83:101–111, 1998. CrossRef
 F. Chudak. Improved approximation algorithms for uncapacitated facility location. In Proceedings of the 6th IPCO Conference, pages 180–194, 1998.
 F. Chudak and D.B. Shmoys. Improved approximation algorithms for the uncapacitated facility location problem. In preparation.
 F. Chudak and D.B. Shmoys. Improved approximation algorithms for a capacitated facility location problem. In Proceedings of the 10th Annual ACMSIAM Symposium on Discrete Algorithms, pages 875–876, 1999.
 G. Cornuéjols, G. Nemhauser, and L. Wolsey. The uncapacitated facility location problem. In P. Mirchandani and R. Francis, editors, Discrete Location Theory, pages 119–171. John Wiley and Sons, Inc., New York, 1990.
 U. Feige. A threshold of ln n for approximating setcover. In Proceedings of the 28th ACM Symposium on Theory of Computing, pages 314–318, 1996.
 S. Guha and S. Khuller. Greedy strikes back: improved facility location algorithms. In Proceedings of the 9th Annual ACMSIAM Symposium on Discrete Algorithms, pages 649–657, 1998.
 M. Korupolu, C. Plaxton, and R. Rajaraman. Analysis of a local search heuristic for facility location problems. In Proceedings of the 9th Annual ACMSIAM Symposium on Discrete Algorithms, pages 1–10, 1998.
 M. Korupolu, C. Plaxton, and R. Rajaraman. Analysis of a local search heuristic for facility location problems. Technical Report 9830, DIMACS, June 1998. Available from http://dimacs.rutgers.edu/TechnicalReports/1998.html.
 E. Lawler. Combinatorial Optimization: Networks and Matroids. Holt, Rinehart, and Winston, New York, 1976.
 C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. JACM 41:960–981, 1994. CrossRef
 P. Mirchandani and R. Francis, eds. Discrete Location Theory. John Wiley and Sons, Inc., New York, 1990.
 G.L. Nemhauser, L.A. Wolsey, and M.L. Fisher. An analysis of approximations for maximizing submodular set functions — I. Mathematical Programming 14:265–294, 1978. CrossRef
 R. Raz and S. Safra. A subconstant errorprobability lowdegree test, and a subconstant errorprobability PCP characterization of NP. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 475–484, 1997.
 D. Shmoys, É. Tardos, and K. Aardal. Approximation algorithms for facility location problems. In Proceedings of the 29th ACM Symposium on Theory of Computing, pages 265–274, 1997.
 M. Sviridenko, July, 1998. Personal communication.
 Title
 Improved Approximation Algorithms for Capacitated Facility Location Problems
 Book Title
 Integer Programming and Combinatorial Optimization
 Book Subtitle
 7th International IPCO Conference Graz, Austria, June 9–11, 1999 Proceedings
 Pages
 pp 99113
 Copyright
 1999
 DOI
 10.1007/3540487778_8
 Print ISBN
 9783540660194
 Online ISBN
 9783540487777
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 1610
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag Berlin Heidelberg
 Additional Links
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 Editors

 Gérard Cornuéjols ^{(4)}
 Rainer E. Burkard ^{(5)}
 Gerhard J. Woeginger ^{(5)}
 Editor Affiliations

 4. GSIA, Carnegie Mellon University
 5. Institut für Mathematik, Technische Universität Graz
 Authors

 Fabián A. Chudak ^{(6)}
 David P. Williamson ^{(7)}
 Author Affiliations

 6. IBM T.J. Watson Research Center, Room 36241, P.O. Box 218, Yorktown Heights, NY, 10598
 7. IBM T.J. Watson Research Center, Room 33219, P.O. Box 218, Yorktown Heights, NY, 10598
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