Abstract
A dynamic network is a directed graph in which arcs have capacities and transit times. In this paper, we consider the evacuation problem in dynamic networks. In this problem, we are given a dynamic network with a single sink vertex in which each vertex except the sink vertex has a supply. Then the goal of this problem is to find the minimum time limit T such that we can send all the supplies to the sink vertex by T. In this paper, we propose a discrete Newton method for the evacuation problem. First, we prove that the number of iterations of this method is at most the number of vertices of the input dynamic network. Then we propose theoretical and practical implementation of this method. The theoretical implementation is based on submodular function minimization, and the practical implementation is based on maximum flow computations in time-expanded networks. Finally, we compare the proposed practical implementation with an algorithm using a binary search in time-expanded networks in computational experiments.
| Original language | English |
|---|---|
| Pages (from-to) | 510-519 |
| Number of pages | 10 |
| Journal | Theoretical Computer Science |
| Volume | 795 |
| DOIs | |
| Publication status | Published - Nov 26 2019 |
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All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Computer Science(all)
Cite this
Discrete Newton methods for the evacuation problem. / Kamiyama, Naoyuki.
In: Theoretical Computer Science, Vol. 795, 26.11.2019, p. 510-519.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Discrete Newton methods for the evacuation problem
AU - Kamiyama, Naoyuki
PY - 2019/11/26
Y1 - 2019/11/26
N2 - A dynamic network is a directed graph in which arcs have capacities and transit times. In this paper, we consider the evacuation problem in dynamic networks. In this problem, we are given a dynamic network with a single sink vertex in which each vertex except the sink vertex has a supply. Then the goal of this problem is to find the minimum time limit T such that we can send all the supplies to the sink vertex by T. In this paper, we propose a discrete Newton method for the evacuation problem. First, we prove that the number of iterations of this method is at most the number of vertices of the input dynamic network. Then we propose theoretical and practical implementation of this method. The theoretical implementation is based on submodular function minimization, and the practical implementation is based on maximum flow computations in time-expanded networks. Finally, we compare the proposed practical implementation with an algorithm using a binary search in time-expanded networks in computational experiments.
AB - A dynamic network is a directed graph in which arcs have capacities and transit times. In this paper, we consider the evacuation problem in dynamic networks. In this problem, we are given a dynamic network with a single sink vertex in which each vertex except the sink vertex has a supply. Then the goal of this problem is to find the minimum time limit T such that we can send all the supplies to the sink vertex by T. In this paper, we propose a discrete Newton method for the evacuation problem. First, we prove that the number of iterations of this method is at most the number of vertices of the input dynamic network. Then we propose theoretical and practical implementation of this method. The theoretical implementation is based on submodular function minimization, and the practical implementation is based on maximum flow computations in time-expanded networks. Finally, we compare the proposed practical implementation with an algorithm using a binary search in time-expanded networks in computational experiments.
UR - http://www.scopus.com/inward/record.url?scp=85072212428&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85072212428&partnerID=8YFLogxK
U2 - 10.1016/j.tcs.2019.08.004
DO - 10.1016/j.tcs.2019.08.004
M3 - Article
AN - SCOPUS:85072212428
VL - 795
SP - 510
EP - 519
JO - Theoretical Computer Science
JF - Theoretical Computer Science
SN - 0304-3975
ER -