Abstract
We study the problem of Fault-Tolerant Facility Allocation (FTFA) which is a relaxation of the classical Fault-Tolerant Facility Location (FTFL) problem [1]. Given a set of sites, a set of cities, and corresponding facility operating cost at each site as well as connection cost for each site-city pair, FTFA requires to allocate each site a proper number of facilities and further each city a prespecified number of facilities to access. The objective is to find such an allocation that minimizes the total combined cost for facility operating and service accessing. In comparison with the FTFL problem which restricts each site to at most one facility, the FTFA problem is less constrained and therefore incurs less cost which is desirable in application. In this paper, we consider the metric FTFA problem where the given connection costs satisfy triangle inequality and we present a polynomial-time algorithm with approximation factor 1.861 which is better than the best known approximation factor 2.076 for the metric FTFL problem [2].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Jain, K., Vazirani, V.V.: An approximation algorithm for the fault tolerant metric facility location problem. In: Jansen, K., Khuller, S. (eds.) APPROX 2000. LNCS, vol. 1913, pp. 177–182. Springer, Heidelberg (2000)
Swamy, C., Shmoys, D.B.: Fault-tolerant facility location. ACM Trans. Algorithms 4(4), 1–27 (2008)
Pitu, B., Mirchandani, R.L.F. (eds.): Discrete Location Theory. John Wiley, New York (1990)
Guha, S., Meyerson, A., Munagala, K.: Improved algorithms for fault tolerant facility location. In: SODA 2001: Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms, Philadelphia, PA, USA, Society for Industrial and Applied Mathematics, pp. 636–641 (2001)
Guha, S., Meyerson, A., Munagala, K.: A constant factor approximation algorithm for the fault-tolerant facility location problem. J. Algorithms 48(2), 429–440 (2003)
Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.: A greedy facility location algorithm analyzed using dual fitting. In: Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques, pp. 127–137 (2001)
Jain, K., Mahdian, M., Saberi, A.: A new greedy approach for facility location problems. In: STOC 2002: Proceedings of the thiry-fourth annual ACM symposium on Theory of computing, pp. 731–740. ACM, New York (2002)
Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. Journal of the ACM 50(6), 795–824 (2003)
Cornuejols, G., Fisher, M.L., Nemhauser, G.L.: Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms. Management Science 23(8), 789–810 (1977)
Hochbaum, D.S.: Heuristics for the fixed cost median problem. Mathematical Programming 22(1), 148–162 (1982)
Shmoys, D.B., Tardos, E., Aardal, K.: Approximation algorithms for facility location problems. In: Proceedings of the 29th Annual ACM Symposium on Theory of Computing, pp. 265–274 (1997)
Lin, J.H., Vitter, J.S.: e-approximations with minimum packing constraint violation. In: STOC 1992: Proceedings of the twenty-fourth annual ACM symposium on Theory of computing, pp. 771–782. ACM, New York (1992)
Chudak, F.A.: Improved approximation algorithms for uncapacitated facility location. In: Bixby, R.E., Boyd, E.A., RÃos-Mercado, R.Z. (eds.) IPCO 1998. LNCS, vol. 1412, pp. 180–194. Springer, Heidelberg (1998)
Sviridenko, M.: An improved approximation algorithm for the metric uncapacitated facility location problem. In: Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization, London, UK, pp. 240–257. Springer, Heidelberg (2002)
Charikar, M., Guha, S.: Improved combinatorial algorithms for facility location problems. SIAM J. Comput. 34(4), 803–824 (2005)
Jain, K., Vazirani, V.V.: Approximation algorithms for metric facility location and k-median problems using the primal-dual schema and Lagrangian relaxation. Journal of the ACM 48(2), 274–296 (2001)
Jain, K., Vazirani, V.V.: Primal-dual approximation algorithms for metric facility location and k-median problems. In: IEEE Symposium on Foundations of Computer Science, pp. 2–13 (1999)
Vazirani, V.V.: Approximation Algorithms. Springer, Berlin (2001)
Mahdian, M., Ye, Y., Zhang, J.: A 1.52-approximation algorithm for the uncapacitated facility location problem. In: Jansen, K., Leonardi, S., Vazirani, V.V. (eds.) APPROX 2002. LNCS, vol. 2462, pp. 229–242. Springer, Heidelberg (2002)
Byrka, J.: An optimal bifactor approximation algorithm for the metric uncapacited facility location problem. In: Charikar, M., Jansen, K., Reingold, O., Rolim, J.D.P. (eds.) RANDOM 2007 and APPROX 2007. LNCS, vol. 4627, pp. 29–43. Springer, Heidelberg (2007)
Chudak, F.A., Shmoys, D.B.: Improved approximation algorithms for the uncapacitated facility location problem. SIAM J. Comput. 33(1), 1–25 (2004)
Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms. Journal of Algorithms 31, 228–248 (1999)
McEliece, R., Rodemich, E., Rumsey, H., Welch, L.: New upper bounds on the rate of a code via the delsarte-macwilliams inequalities. IEEE Transactions on Information Theory 23(2), 157–166 (1977)
Xu, S., Shen, H.: Fault-tolerant k-facility allocation (manuscript)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xu, S., Shen, H. (2009). The Fault-Tolerant Facility Allocation Problem. In: Dong, Y., Du, DZ., Ibarra, O. (eds) Algorithms and Computation. ISAAC 2009. Lecture Notes in Computer Science, vol 5878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10631-6_70
Download citation
DOI: https://doi.org/10.1007/978-3-642-10631-6_70
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-10630-9
Online ISBN: 978-3-642-10631-6
eBook Packages: Computer ScienceComputer Science (R0)