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Main Title: An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times
Author(s): Hall, Alex
Langkau, Katharina
Skutella, Martin
Type: Research Paper
Abstract: Given a network with capacities and transit times on the arcs, the quickest flow problem asks for a "flow over time" that satisfies given demands within minimal time. In the setting of flows over time, flow on arcs may vary over time and the transit time of an arc is the time it takes for flow to travel through this arc. In most real-world applications (such as, e.g., road traffic, communication networks, production systems, etc.), transit times are not fixed but depend on the current flow situation in the network. We consider the model where the transit time of an arc is given as a nondecreasing function of the rate of inflow into the arc. We prove that the quickest s-t-flow problem is NP-hard in this setting and give various approximation results, including a fully polynomial time approximation scheme (FPTAS) for the quickest multicommodity flow problem with bounded cost.
Subject(s): approximation algorithms
dynamic flow
flow over time
graph algorithms
network flow
traffic models
Issue Date: 2003
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 90C27 Combinatorial optimization
90B10 Network models, deterministic
90B20 Traffic problems
90C35 Programming involving graphs or networks
05C85 Graph algorithms
90C59 Approximation methods and heuristics
68W25 Approximation algorithms
68Q25 Analysis of algorithms and problem complexity
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2003, 24
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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