Abstract
The capacitated constraint is a common variant in the field of combinatorial optimization. In the capcitated facility location problem, there is a limitation of service for each facility, that is, capacity. From the view of the approximation algorithm, this variant makes the algorithm difficult to design. Actually, the integral gap of the standard linear program for the capacitated facility location problem is infinite. That is, there is no LP-based constant approximation algorithm. In this work, we consider a special case of the uniform open cost for the capacitated facility location problem. Moreover, all clients are needed to be served. There is another variant of facility location problem called as “robust”. In this paper, we also consider one of the robust forms, named cpacitated facility location problem with penalties. We obtain an LP-based 5.732-approximation algorithm for a uniform capacitated facility location problem with penalties.
Supported by National Natural Science Foundation of China (No. 11971349).
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Aggarwal, A., Louis, A., Bansal, M., Garg, N., Gupta, N., Gupta, S., Jain, S.: A \(3\)-approximation algorithm for the facility location problem with uniform capacities. Math. Program. 141, 527–547 (2013)
An, H.C., Singh, M., Svensson, O.: LP-based algorithms for capacitated facility location. SIAM J. Comput. 46, 272–306 (2017)
Bansal, M., Garg, N., Gupta, N.: A \(5\)-Approximation for Universal Facility Location. In: Ganguly S., Pandya P.K. (eds.) IARCS 2018, LIPIcs, vol. 122, pp. article No. 24. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, Ahmedabad (2018). https://doi.org/10.4230/LIPIcs.FSTTCS.2018.24
Charikar, M., Khuller, S., Mount, D.M., Narasimhan, G.: Algorithms for facility location problems with outliers. In: Proceedings of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 642–651. ACM/SIAM, Washington, DC (2001)
Jain, K., Mahdian, M., Markakis, E., Saberi, A., Vazirani, V.V.: Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP. J. ACM 50, 795–824 (2003)
Li, S.: A \(1.488\)-approximation algorithm for the uncapacitated facility location problem. Inf. Comput. 222, 45–58 (2013)
Li, Y., Du, D., Xiu, N., Xu, D.: Improved approximation algorithms for the facility location problems with linear/submodular penalty. Algorithmica 73, 460–482 (2015)
Levi, R., Shomys, D.B., Swamy, C.: LP-based approximation algorithms for capacitated facility location. Math. Program. 131, 365–379 (2012)
Mahdian, M., Pál, M.: Universal facility location. In: Di Battista, G., Zwick, U. (eds.) ESA 2003. LNCS, vol. 2832, pp. 409–421. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-540-39658-1_38
Pal, M., Tardos, E., Wexler, T.: Facility location with nonuniform hard capacities. In: Proceedings of 42nd Annual Symposium on Foundations of Computer Science, pp. 329–338, IEEE Computer Society, Las Vegas, Nevada, USA (2001)
Guha, S., Khuller, S.: Greedy strike back: improved facility location algorithms. J. Algorithms 31, 228–248 (1999)
Shmoys, D.B.: Tardos E, Aardal K I, Approximation algorithms for facility location problems. In: Proceedings of the 29th Annual ACM Symposium on the Theory of Computing, pp. 265–274. ACM, Texas (1997)
Xu, G., Xu, J.: An improved approximation algorithm for uncapacitated facility location problem with penalties. J. Combinat. Optim. 17, 424–436 (2008)
Zhang, J., Chen, B., Ye, Y.: A multi-exchange local search algorithm for the capacitated facility location problem. Math. Oper. Res. 30, 389–403 (2003)
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Lv, W., Wu, C. (2020). An LP-Rounding Based Algorithm for a Uniform Capacitated Facility Location Problem with Penalties. In: Li, M. (eds) Frontiers in Algorithmics. FAW 2020. Lecture Notes in Computer Science(), vol 12340. Springer, Cham. https://doi.org/10.1007/978-3-030-59901-0_12
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DOI: https://doi.org/10.1007/978-3-030-59901-0_12
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