Abstract
Let P be an undirected path graph of n vertices. Each edge of P has a positive length and a constant capacity. Every vertex has a nonnegative supply, which is an unknown value but is known to be in a given interval. The goal is to find a point on P to build a facility and move all vertex supplies to the facility such that the maximum regret is minimized. The previous best algorithm solves the problem in O(nlog2 n) time and O(nlogn) space. In this paper, we present an O(nlogn) time and O(n) space algorithm, and our approach is based on new observations and algorithmic techniques.
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
Averbakh, I., Bereg, S.: Facility location problems with uncertainty on the plane. Discrete Optimization 2, 3–34 (2005)
Averbakh, I., Berman, O.: Minimax regret p-center location on a network with demand uncertainty. Location Science 5, 247–254 (1997)
Averbakh, I., Berman, O.: Algorithms for the robust 1-center problem on a tree. European Journal of Operational Research 123, 292–302 (2000)
Averbakh, I., Berman, O.: Minmax regret median location on a network under uncertainty. INFORMS Journal on Computing 12, 104–110 (2000)
Averbakh, I., Berman, O.: An improved algorithm for the minmax regret median problem on a tree. Networks 2, 97–103 (2003)
Bhattacharya, B., Kameda, T.: A linear time algorithm for computing minmax regret 1-median on a tree. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds.) COCOON 2012. LNCS, vol. 7434, pp. 1–12. Springer, Heidelberg (2012)
Bhattacharya, B., Kameda, T., Song, Z.: Computing minmax regret 1-median on a tree network with positive/Negative vertex weights. In: Chao, K.-M., Hsu, T.-S., Lee, D.-T. (eds.) ISAAC 2012. LNCS, vol. 7676, pp. 588–597. Springer, Heidelberg (2012)
Bhattacharya, B., Kameda, T., Song, Z.: Minmax regret 1-center on a path/cycle/tree. In: Proc. of the Sixth International Conference on Advanced Engineering Computing and Applications in Sciences, pp. 108–113 (2012)
Chen, B., Lin, C.S.: Minmax-regret robust 1-median location on a tree. Networks 31, 93–103 (1998)
Cheng, S.-W., Higashikawa, Y., Katoh, N., Ni, G., Su, B., Xu, Y.: Minimax regret 1-sink location problems in dynamic path networks. In: Chan, T.-H.H., Lau, L.C., Trevisan, L. (eds.) TAMC 2013. LNCS, vol. 7876, pp. 121–132. Springer, Heidelberg (2013)
Conde, E.: A note on the minmax regret centdian location on trees. Operations Research Letters 36, 271–275 (2008)
Kamiyama, N., Katoh, N., Takizawa, A.: An efficient algorithm for evacuation problem in dynamic network flows with uniform arc capacity. Transactions on Information and Systems E89-D (8), 2372–2379 (2006)
Kouvelis, P., Yu, G. (eds.): Robust discrete optimization and its applications. Kluwer Academic Publishers, Dordrecht (1997)
Megiddo, N.: Linear-time algorithms for linear programming in R 3 and related problems. SIAM Journal on Computing 12(4), 759–776 (1983)
Megiddo, N.: Linear programming in linear time when the dimension is fixed. Journal of the ACM 31(1), 114–127 (1984)
Puerto, J., Rodríguez-Chía, A., Tamir, A.: Minimax regret single-facility ordered median location problems on networks. INFORMS Journal on Computing 21, 77–87 (2009)
Yu, H.I., Lin, T.C., Wang, B.F.: Improved algorithms for the minmax-regret 1-center and 1-median problems. ACM Transactions on Algorithms 4(3), article No. 36 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wang, H. (2013). Minmax Regret 1-Facility Location on Uncertain Path Networks. In: Cai, L., Cheng, SW., Lam, TW. (eds) Algorithms and Computation. ISAAC 2013. Lecture Notes in Computer Science, vol 8283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45030-3_68
Download citation
DOI: https://doi.org/10.1007/978-3-642-45030-3_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45029-7
Online ISBN: 978-3-642-45030-3
eBook Packages: Computer ScienceComputer Science (R0)