Abstract
We study the k-level uncapacitated facility location problem, where clients need to be connected with paths crossing open facilities of k types (levels). In this paper we give an approximation algorithm that for any constant k, in polynomial time, delivers solutions of cost at most α k times OPT, where α k is an increasing function of k, with lim k → ∞ α k = 3.
Our algorithm rounds a fractional solution to an extended LP formulation of the problem. The rounding builds upon the technique of iteratively rounding fractional solutions on trees (Garg, Konjevod, and Ravi SODA’98) originally used for the group Steiner tree problem.
We improve the approximation ratio for k-UFL for all k ≥ 3, in particular we obtain the ratio equal 2.02, 2.14, and 2.24 for k = 3,4, and 5.
This is a preview of subscription content, log in via an institution to check access.
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
Aardal, K., Chudak, F., Shmoys, D.: A 3-Approximation Algorithm for the k-Level Uncapacitated Facility Location Problem. Inf. Process. Lett. 72(5-6), 161–167 (1999)
Aardal, K., Tardos, E., Shmoys, D.: Approximation Algorithms for Facility Location Problems (Extended Abstract). In: STOC 1997, pp. 265–274 (1997)
Ageev, A., Ye, Y., Zhang, J.: Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem. SIAM J. Discrete Math. 18(1), 207–217 (2004)
Byrka, J., Aardal, K.: An Optimal Bifactor Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. SIAM J. Comput. 39(6), 2212–2231 (2010)
Byrka, J., Ghodsi, M., Srinivasan, A.: LP-rounding algorithms for facility-location problems CoRR, abs/1007.3611 (2010)
Chudak, F., Shmoys, D.: Improved Approximation Algorithms for the Uncapacitated Facility Location Problem. SIAM J. Comput. 33(1), 1–25 (2003)
Garg, N., Konjevod, G., Ravi, R.: A polylogarithmic approximation algorithm for the group Steiner tree problem. In: SODA 1998, pp. 253–259 (1998)
Guha, S., Khuller, S.: Greedy strikes back: Improved facility location algorithms
Krishnaswamy, R., Sviridenko, M.: Inapproximability of the multi-level uncapacitated facility location problem. SODA 2012 31(1), 718–734 (1999); Journal of Algorithms 31(1), 228–248 (1999)
Li, S.: A 1.488 Approximation Algorithm for the Uncapacitated Facility Location Problem. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 77–88. Springer, Heidelberg (2011)
Sviridenko, M.: An Improved Approximation Algorithm for the Metric Uncapacitated Facility Location Problem. In: Cook, W.J., Schulz, A.S. (eds.) IPCO 2002. LNCS, vol. 2337, pp. 240–257. Springer, Heidelberg (2002)
Zhang, J.: Approximating the two-level facility location problem via a quasi-greedy approach. In: SODA 2004, pp. 808–817 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Byrka, J., Rybicki, B. (2012). Improved LP-Rounding Approximation Algorithm for k-level Uncapacitated Facility Location. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_14
Download citation
DOI: https://doi.org/10.1007/978-3-642-31594-7_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31593-0
Online ISBN: 978-3-642-31594-7
eBook Packages: Computer ScienceComputer Science (R0)