In this paper, we consider the evacuation problem for a network which consists of a directed graph with capacities and transit times on its arcs. This problem can be solved by the algorithm of Hoppe and Tardos [1] in polynomial time. However their running time is high-order polynomial, and hence is not practical in general. Thus it is necessary to devise a faster algorithm for a tractable and practically useful subclass of this problem. In this paper, we consider a dynamic network with a single sink s such that (i) for each vertex v the sum of transit times of arcs on any path from v to s takes the same value, and (ii) for each vertex v the minimum v-s cut is determined by the arcs incident to s whose tails are reachable from v. We propose an efficient algorithm for this network problem. This class of networks is a generalization of the grid network studied in the paper [2]. © Springer-Verlag Berlin Heidelberg 2007.
CITATION STYLE
Kamiyama, N., Katoh, N., & Takizawa, A. (2007). An efficient algorithm for the evacuation problem in a certain class of a network with uniform path-lengths. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4508 LNCS, pp. 178–190). Springer Verlag. https://doi.org/10.1007/978-3-540-72870-2_17
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