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An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times

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Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques (RANDOM 2003, APPROX 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2764))

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 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.

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Author information

Authors and Affiliations

  1. Institut TIK, Gloriastrasse 35, ETH Zentrum, 8092, Zurich, Switzerland

    Alex Hall

  2. Institut für Mathematik, TU Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Katharina Langkau

  3. Max-Planck Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Martin Skutella

Authors
  1. Alex Hall
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  2. Katharina Langkau
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  3. Martin Skutella
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Editor information

Editors and Affiliations

  1. Computer Science Department, Princeton University, 35 Olden Street, 08540, Princeton, NJ

    Sanjeev Arora

  2. Institute for Computer Science, University of Kiel, Olshausenstrasse 40, 24118, Kiel, Germany

    Klaus Jansen

  3. Battelle Bâtiment A, Centre Universitaire d’Informatique, Route de Drize 7, 1227, Carouge, Geneva, Switzerland

    José D. P. Rolim

  4. University of California, Los Angeles

    Amit Sahai

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© 2003 Springer-Verlag Berlin Heidelberg

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Hall, A., Langkau, K., Skutella, M. (2003). An FPTAS for Quickest Multicommodity Flows with Inflow-Dependent Transit Times. In: Arora, S., Jansen, K., Rolim, J.D.P., Sahai, A. (eds) Approximation, Randomization, and Combinatorial Optimization.. Algorithms and Techniques. RANDOM APPROX 2003 2003. Lecture Notes in Computer Science, vol 2764. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45198-3_7

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  • DOI: https://doi.org/10.1007/978-3-540-45198-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40770-6

  • Online ISBN: 978-3-540-45198-3

  • eBook Packages: Springer Book Archive

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