An efficient algorithm for the evacuation problem in a certain class of networks with uniform path-lengths

Naoyuki Kamiyama, Naoki Katoh, Atsushi Takizawa

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

In this paper, we consider the evacuation problem in 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 [B. Hoppe, É. Tardos, The quickest transshipment problem, Math. Oper. Res. 25(1) (2000) 36-62] 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 network with a sink s such that (i) for each vertex v ≠ s the sum of the transit times of arcs on any path from v to s takes the same value, and (ii) for each vertex v ≠ s the minimum v-s cut is determined by the arcs incident to s whose tails are reachable from v. This class of networks is a generalization of grid networks studied in the paper [N. Kamiyama, N. Katoh, A. Takizawa, An efficient algorithm for evacuation problem in dynamic network flows with uniform arc capacity, IEICE Trans. Infrom. Syst. E89-D (8) (2006) 2372-2379]. We propose an efficient algorithm for this network problem.

Original languageEnglish
Pages (from-to)3665-3677
Number of pages13
JournalDiscrete Applied Mathematics
Volume157
Issue number17
DOIs
Publication statusPublished - Oct 28 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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