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International Colloquium on Automata, Languages, and Programming

ICALP 2003: Automata, Languages and Programming pp 397–409Cite as

Multicommodity Flows over Time: Efficient Algorithms and Complexity

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2719))

Abstract

Flow variation over time is an important feature in network flow problems arising in various applications such as road or air traffic control, production systems, communication networks (e.g., the Internet), and financial flows. The common characteristic are networks with capacities and transit times on the arcs which specify the amount of time it takes for flow to travel through a particular arc. Moreover, in contrast to static flow problems, flow values on arcs may change with time in these networks.

While the ‘maximum s-t-flow over time’ problem can be solved efficiently and ‘min-cost flows over time’ are known to be NP-hard, the complexity of (fractional) ‘multicommodity flows over time’ has been open for many years. We prove that this problem is NP-hard, even for series-parallel networks, and present new and efficient algorithms under certain assumptions on the transit times or on the network topology. As a result, we can draw a complete picture of the complexity landscape for flow over time problems.

Supported by the joint Berlin/Zurich graduate program Combinatorics, Geometry, and Computation (CGC), financed by ETH Zurich and the German Science Foundation (DFG)

Supported in part by the EU Thematic Networks APPOL I & II, Approximation and Online Algorithms, IST-1999-14084, IST-2001-30012.

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References

  1. J. E. Aronson. A survey of dynamic network flows. Annals of Operations Research, 20:1–66, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  2. R. E. Burkard, K. Dlaska, and B. Klinz. The quickest flow problem. ZOR — Methods and Models of Operations Research, 37:31–58, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  3. T. Erlebach and K. Jansen. Call scheduling in trees, rings and meshes. In Proceedings of the 30th Hawaii International Conference on System Sciences, pages 221–222. IEEE Computer Society Press, 1997.

    Google Scholar 

  4. L. Fleischer and M. Skutella. The quickest multicommodity flow problem. In W. J. Cook and A. S. Schulz, editors, Integer Programming and Combinatorial Optimization, volume 2337 of Lecture Notes in Computer Science, pages 36–53. Springer, Berlin, 2002.

    Google Scholar 

  5. L. Fleischer and M. Skutella. Minimum cost flows over time without intermediate storage. In Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 66–75, Baltimore, MD, 2003.

    Google Scholar 

  6. L. K. Fleischer and É Tardos. Efficient continuous-time dynamic network flow algorithms. Operations Research Letters, 23:71–80, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  7. L. R. Ford and D. R. Fulkerson. Constructing maximal dynamic flows from static flows. Operations Research, 6:419–433, 1958.

    Article  MathSciNet  Google Scholar 

  8. L. R. Ford and D. R. Fulkerson. Flows in Networks. Princeton University Press, Princeton, NJ, 1962.

    MATH  Google Scholar 

  9. B. Hoppe. Efficient dynamic network flow algorithms. PhD thesis, Cornell University, 1995.

    Google Scholar 

  10. B. Hoppe and É. Tardos. The quickest transshipment problem. Mathematics of Operations Research, 25:36–62, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Klinz and G. J. Woeginger. Minimum cost dynamic flows: The series-parallel case. In E. Balas and J. Clausen, editors, Integer Programming and Combinatorial Optimization, volume 920 of Lecture Notes in Computer Science, pages 329–343. Springer, Berlin, 1995.

    Google Scholar 

  12. N. Megiddo. Combinatorial optimization with rational objective functions. Mathematics of Operations Research, 4:414–424, 1979.

    MATH  MathSciNet  Google Scholar 

  13. W. B. Powell, P. Jaillet, and A. Odoni. Stochastic and dynamic networks and routing. In M. O. Ball, T. L. Magnanti, C. L. Monma, and G. L. Nemhauser, editors, Network Routing, volume 8 of Handbooks in Operations Research and Management Science, chapter 3, pages 141–295. North-Holland, Amsterdam, The Netherlands, 1995.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Computer Engineering and Networks Laboratory (TIK), ETH Zentrum, Gloriastrasse 35, 8092, Zurich, Switzerland

    Alex Hall

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

    Steffen Hippler

  3. Algorithms and Complexity Group, Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123, Saarbrücken, Germany

    Martin Skutella

Authors
  1. Alex Hall
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  2. Steffen Hippler
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  3. Martin Skutella
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Computer Science, Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Jos C. M. Baeten

  2. School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA, 30332-0205, USA

    Jan Karel Lenstra

  3. Department of Information Technology, Uppsala University, P.O. Box 337, 75105, Uppsala, Sweden

    Joachim Parrow

  4. Faculty of Electrical Engineering, Mathematics and Computer Science, University of Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    Gerhard J. Woeginger

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© 2003 Springer-Verlag Berlin Heidelberg

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Hall, A., Hippler, S., Skutella, M. (2003). Multicommodity Flows over Time: Efficient Algorithms and Complexity. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds) Automata, Languages and Programming. ICALP 2003. Lecture Notes in Computer Science, vol 2719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45061-0_33

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  • DOI: https://doi.org/10.1007/3-540-45061-0_33

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40493-4

  • Online ISBN: 978-3-540-45061-0

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