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Competitive Online Multicommodity Routing

  • Tobias Harks
  • Stefan Heinz
  • Marc E. Pfetsch
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4368)

Abstract

In this paper we study online multicommodity minimum cost routing problems in networks, where commodities have to be routed sequentially. The flow of each commodity can be split on several paths. Arcs are equipped with load dependent price functions defining routing costs. We discuss a greedy online algorithm that routes each commodity by minimizing a convex cost function that only depends on the demands previously routed. We present a competitive analysis of this algorithm showing that for affine linear price functions this algorithm is \(\tfrac{4K}{2+K}\)-competitive, where K is the number of commodities. For the parallel arc case, this algorithm is optimal. Without restrictions on the price functions and network, no algorithm is competitive. Finally, we investigate a variant in which the demands have to be routed unsplittably.

Keywords

Competitive Ratio Online Algorithm Single Path Price Function Competitive Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Moy, J.T.: OSPF: Anatomy of an Internet Routing Protocol. Addison-Wesley, Reading (1999)Google Scholar
  2. 2.
    Cisco: OSPF Design Guide (2006), Documentation available at http://www.cisco.com/en/US/tech/tk365
  3. 3.
    Yahaya, A., Suda, T.: iREX: Inter-domain QoS Automation using Economics. In: Proceedings of IEEE CCNC (2006)Google Scholar
  4. 4.
    Yahaya, A., Harks, T., Suda, T.: iREX: Efficient Inter-domain QoS Automation using Economics. In: Proceedings of IEEE Globecom (2006)Google Scholar
  5. 5.
    Fortz, B., Thorup, M.: Optimizing OSPF/IS-IS weights in a changing world. IEEE JSAC 20, 756–767 (2002)Google Scholar
  6. 6.
    Fortz, B., Thorup, M.: Increasing internet capacity using local search. Computational Optimization and Applications 29, 13–48 (2004)MATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49, 236–259 (2002)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Correa, J.R., Schulz, A.S., Stier Moses, N.E.: Selfish routing in capacitated networks. Math. Oper. Res. 29, 961–976 (2004)MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Fiat, A., Woeginger, G.J. (eds.): Dagstuhl Seminar 1996. LNCS, vol. 1442. Springer, Heidelberg (1998)MATHGoogle Scholar
  10. 10.
    Awerbuch, B., Azar, Y., Plotkin, S.: Throughput-competitive on-line routing. In: 34th Annual Symposium on Foundations of Computer Science (FOCS), Palo Alto, pp. 32–40. IEEE, Los Alamitos (1993)Google Scholar
  11. 11.
    Grötschel, M., Lovász, L., Schrijver, A.: Geometric Algorithms and Combinatorial Optimization. Algorithms and Combinatorics, 2nd edn., vol. 2. Springer, Heidelberg (1993)Google Scholar
  12. 12.
    Dafermos, S., Sparrow, F.: The traffic assignment problem for a general network. J. Res. Natl. Bur. Stand., Sect. B 73, 91–118 (1969)MATHMathSciNetGoogle Scholar
  13. 13.
    Borodin, A., El-Yaniv, R.: Online Computation and Competitive Analysis. Cambridge University Press, Cambridge (1998)MATHGoogle Scholar
  14. 14.
    Garey, M.R., Johnson, D.S.: Computers and Intractability. A Guide to the Theory of NP-Completeness. W. H. Freeman and Company, New York (1979)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tobias Harks
    • 1
  • Stefan Heinz
    • 1
  • Marc E. Pfetsch
    • 1
  1. 1.Konrad-Zuse-Zentrum für Informationstechnik BerlinBerlinGermany

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