Abstract
This paper considers the k-sink location problem in dynamic path networks. In our model, a dynamic path network consists of an undirected path with positive edge lengths, uniform edge capacity, and positive vertex supplies. Here, each vertex supply corresponds to a set of evacuees. Then, the problem requires to find the optimal location of k sinks in a given path so that each evacuee is sent to one of k sinks. Let x denote a k-sink location. Under the optimal evacuation for a given x, there exists a (k − 1)-dimensional vector d, called (k − 1)-divider, such that each component represents the boundary dividing all evacuees between adjacent two sinks into two groups, i.e., all supplies in one group evacuate to the left sink and all supplies in the other group evacuate to the right sink. Therefore, the goal is to find x and d which minimize the maximum cost or the total cost, which are denoted by the minimax problem and the minisum problem, respectively. We study the k-sink location problem in dynamic path networks with continuous model, and prove that the minimax problem can be solved in O(kn logn) time and the minisum problem can be solved in O(kn 2) time, where n is the number of vertices in the given network.
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
Chen, D., Chen, R.: A relaxation-based algorithm for solving the conditional p-center problem. Operations Research Letters 38(3), 215–217 (2010)
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)
Ford Jr., L.R., Fulkerson, D.R.: Constructing maximal dynamic flows from static flows. Operations Research 6, 419–433 (1958)
Higashikawa, Y., Golin, M.J., Katoh, N.: Minimax Regret Sink Location Problem in Dynamic Tree Networks with Uniform Capacity. In: Pal, S.P., Sadakane, K. (eds.) WALCOM 2014. LNCS, vol. 8344, pp. 125–137. Springer, Heidelberg (2014)
Higashikawa, Y., Augustine, J., Cheng, S.W., Golin, M.J., Katoh, N., Ni, G., Su, B., Xu, Y.: Minimax Regret 1-Sink Location Problem in Dynamic Path Networks. Theoretical Computer Science (2014), doi:10.1016/j.tcs.2014.02.010
Kamiyama, N., Katoh, N., Takizawa, A.: An efficient algorithm for evacuation problem in dynamic network flows with uniform arc capacity. IEICE Transactions 89-D(8), 2372–2379 (2006)
Mamada, S., Uno, T., Makino, K., Fujishige, S.: An O(n log2 n) Algorithm for the Optimal Sink Location Problem in Dynamic Tree Networks. Discrete Applied Mathematics 154(16), 2387–2401 (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Higashikawa, Y., Golin, M.J., Katoh, N. (2014). Multiple Sink Location Problems in Dynamic Path Networks. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_14
Download citation
DOI: https://doi.org/10.1007/978-3-319-07956-1_14
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-07955-4
Online ISBN: 978-3-319-07956-1
eBook Packages: Computer ScienceComputer Science (R0)