Abstract
The bounded k-median problem is to select in an undirected graph G = (V,E) a set S of k vertices such that the distance from any vertex v ∈ V to S is at most a given bound d and the average distance from vertices V\S to S is minimized. We present randomized algorithms for several versions of this problem and we prove some inapproximability results. We also study the bounded version of the uncapacitated facility location problem and present extensions of known deterministic algorithms for the unbounded version.
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S. Arora, P. Raghavan, and S. Rao, “Approximation schemes for Euclidean k-medians and related problems,” Proceedings of the 30th Annual ACM Symposium on Theory of Computing, 1998, pp. 106-113.
O. Berman and E.K. Yang, “Medi-center location problems,” Journal of the Operational Research Society, vol. 42, pp. 313-322, 1991.
M. Charikar, S. Guha, É. Tardos, and D.B. Shmoys, “A constant-factor approximation algorithm for the k-median problem,” in Proceedings of the 31st ACM Symposium on Theory of Computing, 1999.
S. Chaudhuri, N. Garg, and R. Ravi, “The p-neighbor k-center problem,” Information Processing Letters, vol. 65, pp. 131-134, 1998.
S.S. Chaudhry, I.C. Choi, and D.K. Smith, “Facility location with and without maximum distance constraints through the p-median problem,” International Journal of Operations and Production Management, vol. 15, pp. 75-81, 1995.
I.C. Choi and S.S. Chaudhry, “The p-median problem with maximum distance constraints: A direct approach,” Location Science, vol. 1, pp. 235-243, 1993.
F. Chudak, “Improved approximation algorithms for uncapacitated facility location,” in Integer Programming and Combinatorial Optimization, R.E. Bixby, E.A. Boyd, and R.Z. Rios-Mercado (Eds.), Lecture Notes in Computer Science, vol. 1412, 1998, pp. 180-194.
G. Cornuejols, G. L. Nemhauser, and L.A. Wolsey, “The uncapacitated facility location problem,” in Discrete Location Theory, P.B. Mirchandani and R.L. Francis (Eds.), Wiley: New York, 1990, pp. 119-171.
Z. Drezner (Ed.), Facility Location. A Survey of Applications and Methods, Springer-Verlag: New York, 1995.
S. Guha and S. Khuller, “Greedy strikes back: Improved facility location algorithms,” in Proceedings of the 9th Annual ACM-SIAM Symposium on Discrete Algorithms, 1998, pp. 649-657.
D.S. Hochbaum and D.B. Shmoys, “A unified approach to approximation algorithms for bottleneck problems,” Journal of the ACM, vol. 33, pp. 533-550, 1986.
A.K. Jain and R.C. Dubes, Algorithms for Clustering Data, Prentice Hall: Englewood, NJ 1981.
S. Khuller, R. Pless, and Y. J. Sussmann, “Fault Tolerant k-center problems,” Theoretical Computer Science, vol. 242, pp. 237-245, 2000.
B.M. Khumawala, “An efficient algorithm for the p-median problem with maximum distance constraint,” Geographical Analysis, vol. 5, pp. 309-321, 1973.
G. Lin and G. Xue, “Balancing shortest-path trees and Steiner minimum trees in the rectilinear plane,” in Proceedings of the 1999 IEEE International Symposium on Circuits and Systems (ISCAS'99), pp. 117-120, vol. VI, 1999.
J.H. Lin and J.S. Vitter, “∈-Approximations with minimum packing constraint violation,” in Proceedings 24th ACM Symposium on Theory of Computing, 1992a, pp. 771-782.
J.H. Lin and J.S. Vitter, “Approximation algorithms for geometric median problems,” Information Processing Letters, vol. 44, pp. 245-249, 1992b.
M.V. Marathe, R. Ravi, R. Sundaram, S.S. Ravi, D.J. Rosenkrantz, and H.B. Hunt III, “Bicriteria network design problems,” Journal of Algorithms, vol. 28, pp. 142-171, 1998.
R. Motwani and P. Raghavan, Randomized Algorithms, Cambridge University Press, New York, 1995.
D.B. Shmoys, É. Tardos, and K. Aardal, “Approximation algorithms for facility location problems,” in Proceedings of the 29th ACM Symposium on Theory of Computing, 1997, pp. 265-274.
C. Toregas, R. Swain, C. ReVelle, and L. Bergman, “The location of emergency service facilities,” Operations Research, vol. 19, pp. 1363-1373, 1971.
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Krysta, P., Solis-Oba, R. Approximation Algorithms for Bounded Facility Location Problems. Journal of Combinatorial Optimization 5, 233–247 (2001). https://doi.org/10.1023/A:1011465419252
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DOI: https://doi.org/10.1023/A:1011465419252