LNCS 2764 An FPTAS for Quickest Multicommodity Flows with Inflow Dependent Transit Times 1st Edition by Alex Hall, Katharina Langkau, Martin Skutella ISBN 3540380450 9783540380450
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Authors:Alex Hall, Katharina Langkau; Martin Skutella , Tags:Approximation; Randomization; and Combinatorial Optimization. Algorithms and Techniques , Author sort:Alex Hall, Katharina Langkau & Skutella, Martin , Languages:Languages:eng , Published:Published:Sep 2003
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Product details:
ISBN 10: 3540380450
ISBN 13: 9783540380450
Author: Alex Hall, Katharina Langkau, Martin Skutella
LNCS 2764 – An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times 1st Edition:
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 an FPTAS for the quickest multicommodity flow problem with bounded cost.
Extended abstract; information on the full version of the paper can be obtained via the authors’ WWW-pages. This work was supported in part by the joint Berlin/Zurich graduate program Combinatorics, Geometry, and Computation (CGC) financed by ETH Zurich and the German Science Foundation grant GRK 588/2 and by the EU Thematic Network APPOL II, Approximation and Online Algorithms, IST-2001-30012.
LNCS 2764 – An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times 1st Edition Table of contents:
1 Introduction
2 Preliminaries
3 The Bow Graph
3.1 A Relaxation of Inflow-Dependent Transit Times
4 A (2 + ε)-Approximation Algorithm for Quickest Flows
4.1 (2 + ε)-Approximate Quickest Weakly Inflow-Preserving Flows
4.2 (2 + ε)-Approximate Quickest Flows with Inflow-Dependent Transit Times
5 An FPTAS for Quickest Flows
5.1 The Algorithm
6 Complexity
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