Computational Optimization and Applications

, Volume 29, Issue 1, pp 13–48 | Cite as

Increasing Internet Capacity Using Local Search

  • Bernard Fortz
  • Mikkel Thorup


Open Shortest Path First (OSPF) is one of the most commonly used intra-domain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow evenly at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network operator. The weights could be set proportional to the physical lengths of the links, but often the main goal is to avoid congestion, i.e. overloading of links, and the standard heuristic recommended by Cisco (a major router vendor) is to make the weight of a link inversely proportional to its capacity.

We study the problem of optimizing OSPF weights for a given a set of projected demands so as to avoid congestion. We show this problem is NP-hard, even for approximation, and propose a local search heuristic to solve it. We also provide worst-case results about the performance of OSPF routing vs. an optimal multi-commodity flow routing. Our numerical experiments compare the results obtained with our local search heuristic to the optimal multi-commodity flow routing, as well as simple and commonly used heuristics for setting the weights. Experiments were done with a proposed next-generation AT&T WorldNet backbone as well as synthetic internetworks.

traffic engineering shortest path routing local search 


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  1. 1.
    E.H.L. Aarts and J.K. Lenstra, Local Search in Combinatorial Optimization. Discrete Mathematics and Optimization Wiley-Interscience: Chichester, England, 1997.Google Scholar
  2. 2.
    D. Applegate and M. Thorup, “Load optimal mpls routing with n+ mlabels,” in Proc. 22nd IEEE Conf. on Computer Communications (INFOCOM), (to appear), 2003.Google Scholar
  3. 3.
    R. Battiti and G. Tecchiolli, “The reactive tabu search,” ORSA Journal on Computing, vol. 6, no. 2, pp. 126–140, 1994.Google Scholar
  4. 4.
    W. Ben-Ameur and E. Gourdin, “Internet routing and related topology issues,” Technical report, France Telecom R&D, 2001.Google Scholar
  5. 5.
    W. Ben-Ameur, N. Michel, E. Gourdin, and B. Liau, “Routing strategies for IP networks,” Telektronikk, vols. 2/3, pp. 145–158, 2001.Google Scholar
  6. 6.
    A. Bley, M. Grötchel, and R. Wessäly, “Design of broadband virtual private networks: Model and heuristics for the B-WiN,” in Proc. DIMACS Workshop on Robust Communication Networks and Survivability, AMSDIMACS Series, vol. 53, 1998, pp. 1–16.Google Scholar
  7. 7.
    L.S. Buriol, M.G.C. Resende, C.C. Ribeiro, and M. Thorup, “A memetic algorithms for OSPF routing,” in Proceedings of the 6th INFORMS Telecom, 2002, pp. 187–188.Google Scholar
  8. 8.
    K. Calvert, M. Doar, and E.W. Zegura, “Modeling internet topology,” IEEE Communications Magazine, vol. 35, no. 6, pp. 160–163, 1997.CrossRefGoogle Scholar
  9. 9.
    W. Carlton and J. Barnes, “A note on hashing functions and tabu search algorithms,” European Journal of Operational Research, vol. 95, pp. 237–239, 1996.CrossRefGoogle Scholar
  10. 10.
    J.L. Carter and M.N. Wegman, “Universal classes of hash functions,” Jounal of Computer and System Sciences, vol. 18, pp. 143–154, 1979.CrossRefGoogle Scholar
  11. 11.
    Cisco, “Configuring OSPF,” 1997, Documentation at[4]univercd/cc/td/doc/product/ software/ios113ed/113ed cr/np1 c/1cospf.htm.Google Scholar
  12. 12.
    S. Cook, “The complexity of theorem proving procedures,” in Proc. 3rd ACMSymp. on Theory of Computing (STOC), 1971, pp. 151–158.Google Scholar
  13. 13.
    M. Dietzfelbinger, “Universal hashing and k-wise independent random variables via integer arithmetic without primes,” in Proc. 13th Symp. on Theoretical Aspects of Computer Science (STACS), LNCS vol. 1046, Springer, 1996, pp. 569–580.Google Scholar
  14. 14.
    M. Ericsson, M. Resende, and P. Pardalos, “A genetic algorithm for the weight setting problem in OSPF routing,” 2001, To appear in J. Combinatorial Optimization in 2002.Google Scholar
  15. 15.
    B. Fortz, J. Rexford, and M. Thorup, “Traffic engineering with traditional IP routing protocols,” IEEE Communications Magazine, vol. 40, no. 10, pp. 118–124, 2002.CrossRefGoogle Scholar
  16. 16.
    B. Fortz and M. Thorup, “Increasing internet capacity using local search,” Technical Report IS-MG 2000/21, Université Libre de Bruxelles, 2000a. 21.html.Google Scholar
  17. 17.
    B. Fortz and M. Thorup, “Internet traffic engineering by optimizing OSPF weights,” in Proc. 19th IEEE Conf. on Computer Communications (INFOCOM), 2000b, pp. 519–528.Google Scholar
  18. 18.
    B. Fortz and M. Thorup, “Optimizing OSPF/IS-IS weights in a changing world,” IEEE Journal on Selected Areas in Communications, vol. 20, no. 4, pp. 756–767, 2002.CrossRefGoogle Scholar
  19. 19.
    D. Frigioni, M. Ioffreda, U. Nanni, and G. Pasqualone, “Experimental analysis of dynamic algorithms for the single-source shortest path problem,” ACM Jounal of Experimental Algorithmics, vol. 3, no. 5, 1998.Google Scholar
  20. 20.
    F. Glover, “Future paths for integer programming and links to artificial intelligence,” Computers & Operations Research, vol. 13, pp. 533–549, 1986.Google Scholar
  21. 21.
    F. Glover, “Tabu search-Part I,” ORSA Journal on Computing, vol. 1, no. 3, pp. 190–206, 1989.Google Scholar
  22. 22.
    F. Glover, “Tabu search-Part II,” ORSA Journal on Computing, vol. 2, no. 1, pp. 4–32, 1990.Google Scholar
  23. 23.
    F. Glover and M. Laguna, Tabu Search, Kluwer Academic Publishers, 1997.Google Scholar
  24. 24.
    J. Hâstad, “Some optimal inapproximability results,” Journal of the ACM, vol. 48, no. 4, pp. 798–859, 2001.CrossRefGoogle Scholar
  25. 25.
    D.E. Knuth, “The Art of Computer Programming III: Sorting and Searching,” Addison-Wesley: Reading, MA, 1973.Google Scholar
  26. 26.
    F. Lin and J. Wang, “Minimax open shortest path first routing algorithms in networks supporing the smds services,” in Proc. IEEE International Conference on Communications (ICC), vol. 2, 1993, pp. 666–670.CrossRefGoogle Scholar
  27. 27.
    D. Mitra and K. Ramakrishnan, “A case study of multiservice, multipriority traffic engineering design for data networks,” in Proc. IEEE GLOBECOM, 1999, pp. 1077–1083.Google Scholar
  28. 28.
    J.T. Moy, OSPF: Anatomy of an Internet Routing Protocal, Addison-Wesley, 1999.Google Scholar
  29. 29.
    G. Ramalingam and T. Reps, “An incremental algorithm for a generalization of the shortest-path problem,” Jounal of Algorithms, vol. 21, no. 2, pp. 267–305, 1996.CrossRefGoogle Scholar
  30. 30.
    M. Rodrigues and K. Ramakrishnan, “Optimal routing in data networks,” Presentation at International Telecommunications Symposium (ITS), Rio de Genero, Brazil, 1994.Google Scholar
  31. 31.
    E.C. Rosen, A. Viswanathan, and R. Callon, “Multiprotocol label switching architecture,” Network Working Group, Internet Draft (work in progress), 1999. Scholar
  32. 32.
    M. Roughan and M. Thorup, “Avoiding ties in shortest path first routing,” Technical report, AT&T Labs-Research, 2002.Google Scholar
  33. 33.
    Sprint, “Sprint IP backbone network and MPLS,” 2002, White Paper library/resources/SprintCiscoMPLS.pdf.Google Scholar
  34. 34.
    M. Thorup, “Even strongly universal hashing is pretty fast,” in Proc. 11th ACM-SIAM Symp. on Discrete Algorithms (SODA), 2000, pp. 496–497.Google Scholar
  35. 35.
    B.M. Waxman, “Routing of multipoint connections,” IEEE Jour. Selected Areas in Communications (Special Issue on Broadband Packet Communications), vol. 6, no. 9, pp. 1617–1622, 1988.Google Scholar
  36. 36.
    D.L. Woodruff and E. Zemel, “Hashing vectors for tabu search,” Annals of Operations Research, vol. 41, pp. 123–137, 1993.Google Scholar
  37. 37.
    X. Xiao, A. Hannan, B. Bailey, and L. Ni, “Traffic engineering with MPLS in the Internet,” IEEE Network Magazine, vol. 14, no. 2, pp. 28–33, 2000.Google Scholar
  38. 38.
    E.W. Zegura, “GT-ITM: Georgia tech internetwork topology models (software),” 1996. edu/fac/Ellen.Zegura/gt-itm/gt-itm.tar.gz.Google Scholar
  39. 39.
    E.W. Zegura, K.L. Calvert, and S. Bhattacharjee, “How to model an internetwork,” in Proc. 15th IEEE Conf. on Computer Communications (INFOCOM), 1996, pp. 594–602.Google Scholar
  40. 40.
    A.L. Zobrist and F.R. Carlson, Jr., “Detection of combined occurrences,” Comm. ACM, vol. 20, no. 1, pp. 31–35, 1977.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Bernard Fortz
    • 1
  • Mikkel Thorup
    • 1
  1. 1.Institut d'Administration et de Gestion, UniversitéLouvain-la-NeuveBelgium

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