Abstract
In this paper we present improved combinatorial approximation algorithms for the k-level facility location problem. First, by modifying the path reduction developed in [2], we obtain a combinatorial algorithm with a performance factor of 3.27 for any k ≥ 2, thus improving the previous bound of 4.56. Then we develop another combinatorial algorithm that has a better performance guarantee and uses the first algorithm as a subroutine. The latter algorithm can be recursively implemented and achieves a guarantee factor h(k), where h(k) is strictly less than 3.27 for any k and tends to 3.27 as k goes to δ. The values of h(k) can be easily computed with an arbitrary accuracy: h(2) ≈ 2.4211, h(3) ≈ 2.8446, h(4) ≈ 3.0565, h(5) ≈ 3.1678 and so on. Thus, for the cases of k = 2 and k = 3 the second combinatorial algorithm ensures an approximation factor significantly better than 3, which is currently the best approximation ratio for the k-level problem provided by the non-combinatorial algorithm due to Aardal, Chudak, and Shmoys [1].
Research was partially supported by the Russian Foundation for Basic Research, project codes 01-01-00786, 02-01-01153, by INTAS, project code 00-217, and by the Programme “Universities of Russia”, project code UR.04.01.012.
Research supported in part by NSF grant DMI-0231600.
Research supported in part by NSF grant DMI-0231600.
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
K. Aardal, F.A. Chudak, and D.B. Shmoys, “A 3-approximation algorithm for the k-level uncapacitated facility location problem,” Information Processing Letters 72 (1999), 161–167.
A. A. Ageev, “Improved approximation algorithms for multilevel facility location problems,” Oper. Res. Letters 30 (2002), 327–332. The conference version appeared in Proceedings of 5th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX 2002), LNCS 2462 (2002), 5–13.
A.F. Bumb and W. Kern, “A simple dual ascent algorithm for the multilevel facility location problem,” 4th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX 2001), LNCS 2129 (2001), 55–62.
E. Kh. Gimadi, personal communication.
S. Guha and S. Kuller, “Greedy strikes back: improved facility location algorithms,” Journal of Algorithms 31 (1999), 228–248.
S. Guha, A. Meyerson, and K. Munagala, “Hierarchical placement and network design problems,” Proceedings of IEEE Symposium on Foundations of Computer Science (FOCS 2000), 2000, 603–612.
K. Jain, M. Mahdian, and A. Saberi, “A new greedy approach for facility location problems”, in: Proceedings of the 34th ACM Symposium on Theory of Computing (STOC’02), Montreal, Quebec, Canada, May 19–21, 2002.
M. Mahdian, E. Markakis, A. Saberi, and V. Vazirani, “A greedy facility location algorithm analyzed using dual fitting”, in: Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX’2001), Berkeley, CA, USA, August 18–20, Lecture Notes in Computer Science, Vol. 2129, 127–137.
M. Mahdian, Y. Ye, and J. Zhang, “Improved approximation algorithms for metric facility location problems,” 5th International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX 2002), LNCS 2462 (2002) 229–242.
A. Meyerson, K. Munagala, and S. Plotkin, “Cost-distance: two-metric network design,” Proceedings of IEEE Symposium on Foundations of Computer Science (FOCS 2000), 2000, 624–630.
D. B. Shmoys, “Approximation algorithms for facility location problems,” 3rd International Workshop on Approximation Algorithms for Combinatorial Optimization (APPROX), LNCS 1913 (2000) 27–33.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ageev, A., Ye, Y., Zhang, J. (2003). Improved Combinatorial Approximation Algorithms for the k-Level Facility Location Problem. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_13
Download citation
DOI: https://doi.org/10.1007/3-540-45061-0_13
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40493-4
Online ISBN: 978-3-540-45061-0
eBook Packages: Springer Book Archive