Cancel‐and‐tighten algorithm for quickest flow problems

Given a directed graph with a capacity and a transit time for each arc and with single source and single sink nodes, the quickest flow problem is to find the minimum time horizon to send a given amount of flow from the source to the sink. This is one of the fundamental dynamic flow problems. Paramet...

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Bibliographic Details
Published in:Networks Vol. 69; no. 2; pp. 179 - 188
Main Authors: Saho, Masahide, Shigeno, Maiko
Format: Journal Article
Language:English
Published: New York Wiley Subscription Services, Inc 01.03.2017
Subjects:
Algorithms
cancel and tighten algorithm
Complexity
Construction costs
cost scaling
dynamic flow
Graph theory
Minimum cost
network optimization
Networks
Polynomials
quickest flow
strongly polynomial time algorithm
Transit time
ISSN:0028-3045, 1097-0037
Online Access:Get full text
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Summary:Given a directed graph with a capacity and a transit time for each arc and with single source and single sink nodes, the quickest flow problem is to find the minimum time horizon to send a given amount of flow from the source to the sink. This is one of the fundamental dynamic flow problems. Parametric search is one of the basic approaches to solving the problem. Recently, Lin and Jaillet (SODA, 2015) proposed an algorithm whose time complexity is the same as that of the minimum cost flow algorithm. Their algorithm employs a cost scaling technique, and its time complexity is weakly polynomial time. In this article, we modify their algorithm by adopting a technique to construct a strongly polynomial time algorithm for solving the minimum cost flow problem. The proposed algorithm runs in O ( n m 2 ( log n ) 2 ) time, where n and m are the numbers of nodes and arcs, respectively. © 2016 Wiley Periodicals, Inc. NETWORKS, Vol. 69(2), 179–188 2017
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ISSN:0028-3045
1097-0037
DOI:10.1002/net.21726