Discrete Newton methods for the evacuation problem

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)510-519
Number of pages10
JournalTheoretical Computer Science
Volume795
DOIs
Publication statusPublished - Nov 26 2019

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Evacuation
Dynamic Networks
Newton-Raphson method
Newton Methods
Vertex of a graph
Function Minimization
Submodular Function
Binary search
Maximum Flow
Directed graphs
Computational Experiments
Directed Graph
Arc of a curve
Iteration
Experiments

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 journalArticle

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