Abstract
Facility location problem is a well established research area within Operations Research. Capacitated facility location problem is one of the most important variants, in which each facility has an upper bound on the demand, i.e., capacity. Moreover, the integrality gap of the natural linear program relaxation for the problem is infinite. Fortunately, the gap is finite when all opening costs for the facilities are the same. We consider a capacity facility location problem with penalties in which it is allowed some customers are not served by facilities and all opening costs are uniform. Based on LP-rounding framework, we propose a 5.732-approximation algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aggarwal A, Louis A, Bansal M, Garg N, Gupta N, Gupta S, Jain S (2013) A \(3\)-approximation algorithm for the facility location problem with uniform capacities. Math Programm 141:527–547
An HC, Singh M (2017) Svensson, O: LP-based algorithms for capacitated facility location. SIAM J Comput 46:272–306
Angel E, Thang NK, Regnault D (2015) Improved local search for universal facility location. J Comb Optim 291:237–246
Arya V, Garg N, Khandekar R, Meyerson A, Munagala K, Pandit V (2004) Local search heuristics for \(k\)-median and facility location problems. SIAM J Comput 33(3):544–562
Charikar M, Khuller S, Mount D M, Narasimhan G. Algorithms for facility location problems with outliers, in Proceedings of SODA, pp. 642-651 (2001)
Chudak FA, Shmoys DB (2003) Improved approximation algorithms for the uncapacitated facility location problem. SIAM J Comput 33:1–25
Chudak, F.A., Shmoys D.B.: Improved approximation algorithms for capacitated facility location problems. In: Proceedings of the Tenth annual ACM-SIAM symposium on discrete algorithms, pp. 17-19 (1999)
Korupolu MR, Plaxton CG, Rajaraman R (2000) Analysis of a local search heuristic for facility location problems. J Algorithms 371:146–188
Guha S, Khuller S (1999) Greedy strikes back: improved facility location algorithms. J Algorithms 311:228–248
Hochbaum DS (1982) Heuristics for the fixed cost median problem. Math Program 22:148–162
Jain K, Mahdian M, Markakis E, Saberi E, Vazirani VV (2003) Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. J ACM 50(6):795–824
Jain K, Vazirani VV (2001) Approximation algorithms for metric facility location and \(k\)-median problems using the primal-dual schema and Lagrangian relaxation. J ACM 48(2):274–296
Levi R, Shomys DB, Swamy C (2012) LP-based approximation algorithms for capacitated facility location. Math Program 131:365–379
Li S (2013) A \(1.488\) approximation algorithm for the uncapacitated facility location problem. Inform Comput 222:45–58
Li Y, Du D, Xiu N, Xu D (2015) Improved approximation algorithms for the facility location problems with linear/submodular penalty. Algorithmica 73:460–482
Pal, M., Tardos, T., Wexler, T (2001) Facility location with nonuniform hard capacities. In: Proceedings 42nd IEEE symposium on foundations of computer science, pp. 329-338
Shmoys DB, Tardos É, Aardal KI (1997) Approximation algorithms for facility location problems. In: Proceedings of the 29th annual ACM symposium on theory of computing, pp. 265-274
Sviridenko M, cited as personal communication in [6], 1998 Jul
Xu G, Xu J (2008) An improved approximation algorithm for uncapacitated facility location problem with penalties. J Comb Optim 17:424–436
Zhang J, Chen B, Ye Y (2005) A multiexchange local search algorithm for the capacitated facility location problem. Math Op Res 30642:219–233
Funding
We would like to thank the referees for their obvious diligence, thoughtful and insightful comments. These comments help us to make the paper better. The second author is supported by National Natural Science Foundation of China (No. 11971349).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supported by National Natural Science Foundation of China (No. 11971349). The previous version of the paper is accepted by The Fourteenth International Frontiers of Algorithmics Workshop (FAW 2020).
Rights and permissions
About this article
Cite this article
Lv, W., Wu, C. An LP-rounding based algorithm for a capacitated uniform facility location problem with penalties. J Comb Optim 41, 888–904 (2021). https://doi.org/10.1007/s10878-021-00726-0
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10878-021-00726-0