Abstract
The Unbounded Facility Location Problem on outerplanar graphs is considered. The algorithm with time complexity \( O(n m^3)\) was known for solving this problem, where \( n\) is the number of vertices, \( m\) is the number of possible plant locations. Using some properties of maximal outerplanar graphs (binary 2-trees) and the existence of an optimal solution with a family of centrally-connected service areas, the recurrence relations are obtained allowing to design an algorithm which can solve the problem in \( O(n m^{2.5})\) time.
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.: Graphs, matrices and the simple plant location problem (in Russian). Upravlyaemye Sistemy 29, 3–12 (1989)
Ageev, A.A.: A polynomial algorithm for solving the location problem on a series-parallel network (in Russian). Upravlyaemye Sistemy 30, 3–6 (1990)
Billionet, A., Costa, M.-C.: Solving the uncapacitated plant location problem on trees. Discrete Appl. Math. 49(1–3), 51–59 (1994)
Gadegaard, S.L.: Discrete Location Problems. A Ph.D. dissertation, 150 p. Aarhus University Department of Economics and Business Economics (2016)
Garey, M.R., Johnson, D.S.: Computers and Intractability. Freeman, San Francisco (1979). 338 p
Gimadi, E.K.: An efficient algorithm for solving plant location problem with service regions connected with respect to an acyclic network (in Russian). Upravlyaemye Sistemy 23, 12–23 (1983)
Gimadi, E.K.: The problem of location on a network with centrally connected service areas (in Russian). Upravlyaemye Sistemy 25, 38–47 (1984)
Hassin, R., Tamir, A.: Efficient algorithm for optimization and selection on series-parallel graphs. SIAM J. Algebraic Discrete Methods 7(3), 379–389 (1986)
Kolen, A.: Solving covering problems and the uncapacitated plant location on the trees. Eur. J. Oper. Res. 12(3), 266–278 (1983)
Laporte, G., Nickel, S., da Gama, F.S. (eds.): Location Science. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-13111-5. 644 p.
Mirchandani, P.B., Francis, R.L. (eds.): Discrete Location Theory. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York/Chichester/Brisbane/Toronto/Singapore (1990). 555 p
Trubin, V.A.: An efficient algorithm for plant locating on trees (in Russian). Dokl. AN SSSR 231(3), 547–550 (1976)
Ulukan, Z., Demircioglu, E.: A survey of discrete facility location problems. Int. J. Soc. Behav. Educ. Econ. Bus. Ind. Eng. 9(7), 2487–2492 (2015)
Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. SIAM J. Comput. 11(2), 298–313 (1982)
Acknowledgments
The author was supported by the Russian Science Foundation, project no. 16-11-10041.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this paper
Cite this paper
Gimadi, E. (2018). An Exact Polynomial Algorithm for the Outerplanar Facility Location Problem with Improved Time Complexity. In: van der Aalst, W., et al. Analysis of Images, Social Networks and Texts. AIST 2017. Lecture Notes in Computer Science(), vol 10716. Springer, Cham. https://doi.org/10.1007/978-3-319-73013-4_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-73013-4_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73012-7
Online ISBN: 978-3-319-73013-4
eBook Packages: Computer ScienceComputer Science (R0)