Abstract
We show that the facility location problem with uniform hard capacities can be solved by the Ageev’s algorithm in \(O(m^3n^2)\) time, where m is the number of facilities and n is the number of clients. This improves the results \(O(m^5 n^2)\) of Ageev in 2004 and \(O(m^4n^2)\) of Ageev, Gimadi, and Kurochkin in 2009.
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
References
Ageev, A.A.: A polynomial-time algorithm for the facility location problem with uniform hard capacities on path graph. In: Proceedings of the 2nd International Workshop on Discrete Optimization Methods in Production and Logistics, DOM 2004, Omsk, pp. 28–32 (2004)
Ageev, A.A., Gimadi, E.Kh., Kurochkin, A.A.: A polynomial-time algorithm for the facility location problem on the path with uniform hard capacities. In: Discrete Analysis and Operation Research. IM SO RAN, Novosibirsk, vol. 16, no. 5, pp. 3–17 (2009)
Chudak, F.A., Williamson, D.P.: Improved approximation algorithms for capacitated facility location problems. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds.) IPCO 1999. LNCS, vol. 1610, pp. 99–113. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48777-8_8
Cornuéjols, G., Nemhauser, G.L., Wolsey, L.A.: The uncapacitated facility location problem. In: Mirchandani, P., Francis, R. (eds.) Discrete Location Theory, pp. 119–171. Wiley, New York (1990)
Garey, M.R., Johnson, D.S.: Computers and Intractablity. Freeman, San Francisco (1979)
Korupolu, M.R., Plaxton, C.G., Rajaraman, R.: Analysis of a local search heuristic Algorithms, pp. 1–10 (1998)
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
Mirchandani, P., Kohli, R., Tamir, A.: Capacitated location problems on a line. Transp. Sci. 30(1), 75–80 (1996)
Pál, M., Tardos, E., Wexler, T.: Facility location with hard capacities. In: Proceeding of the 42nd Annual Symposium on Foundations of Computer Science (2001)
Zhang, J., Chen, B., Ye, Y.: A multi-exchange local search algorithm for the capacitated facility location problem. Manuscript (2003)
Acknowledgments
Sections 1 and 2 of this research were supported by the Russian Foundation for Basic Research (project 16-07-00168), by the Russian Ministry of Science and Education under the 5–100 Excellence Programme and by the program of fundamental scientific researches of the SB RAS I.5.1. Section 3 is supported by the Russian Science Foundation (project 16-11-10041).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Gimadi, E.K., Kurochkina, A.A. (2019). Time Complexity of the Ageev’s Algorithm to Solve the Uniform Hard Capacities Facility Location Problem. In: Evtushenko, Y., Jaćimović, M., Khachay, M., Kochetov, Y., Malkova, V., Posypkin, M. (eds) Optimization and Applications. OPTIMA 2018. Communications in Computer and Information Science, vol 974. Springer, Cham. https://doi.org/10.1007/978-3-030-10934-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-10934-9_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10933-2
Online ISBN: 978-3-030-10934-9
eBook Packages: Computer ScienceComputer Science (R0)