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An Integer Programming Algorithm for Routing Optimization in IP Networks

Abstract

Most data networks nowadays use shortest path protocols to route the traffic. Given administrative routing lengths for the links of the network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination.

In this paper, we present an integer programming algorithm for the minimum congestion unsplittable shortest path routing problem, which arises in the operational planning of such networks. Given a capacitated directed graph and a set of communication demands, the goal is to find routing lengths that define a unique shortest path for each demand and minimize the maximum congestion over all links in the resulting routing. We illustrate the general decomposition approach our algorithm is based on, present the integer and linear programming models used to solve the master and the client problem, and discuss the most important implementational aspects. Finally, we report computational results for various benchmark problems, which demonstrate the efficiency of our algorithm.

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References

  1. 1.

    Atesio GmbH, Sophie-Taeuber-Arp-Weg 27, D-12205 Berlin, Germany: Discnet—Network optimization software library (2000–2005). http://www.atesio.de

  2. 2.

    Ben-Ameur, W., Gourdin, E.: Internet routing and related topology issues. SIAM J. Discrete Math. 17, 18–49 (2003)

  3. 3.

    Bley, A.: A Lagrangian approach for integrated network design and routing in IP networks. In: Proceedings of the 1st International Network Optimization Conference (INOC 2003), Paris, France, pp. 107–113 (2003)

  4. 4.

    Bley, A.: Inapproximability results for the inverse shortest paths problem with integer lengths and unique shortest paths. Networks 50, 29–36 (2007)

  5. 5.

    Bley, A.: Routing and capacity optimization for IP networks. PhD thesis, Technische Universität Berlin (2007)

  6. 6.

    Bley, A.: Approximability of unsplittable shortest path routing problems. Networks 54(1), 23–46 (2009)

  7. 7.

    Bley, A.: On the hardness of finding small shortest path routing conflicts. In: Proceedings of the 4th International Network Optimization Conference (INOC 2009), Pisa, Italy (2009)

  8. 8.

    Bley, A., Fortz, B., Gourdin, E., Holmberg, K., Klopfenstein, O., Pióro, M., Tomaszewski, A., Ümit, H.: Optimization of OSPF routing in IP networks. In: Koster, A., Muñoz, X. (eds.) Graphs and Algorithms in Communication Networks: Studies in Broadband, Optical, Wireless and Ad Hoc Networks, pp. 199–240. Springer, Berlin (2009)

  9. 9.

    Bley, A., Grötschel, M., Wessäly, R.: Design of broadband virtual private networks: Model and heuristics for the B-WiN. In: Dean, N., Hsu, D., Ravi, R. (eds.) Robust Communication Networks: Interconnection and Survivability. DIMACS Series in Discrete Mathematics and Theoretical Computer Science, vol. 53, pp. 1–16. American Mathematical Society, Providence (1998)

  10. 10.

    Bley, A., Koch, T.: Integer programming approaches to access and backbone IP-network planning. In: Modeling, Simulation and Optimization of Complex Processes: Proceedings of the 3rd International Conference on High Performance Scientific Computing, pp. 87–110. Hanoi, Vietnam (2006)

  11. 11.

    Bley, A., Pattloch, M.: Modellierung und Optimierung der X-WiN Plattform. DFN-Mitteilungen 67, 4–7 (2005)

  12. 12.

    Bourquia, N., Ben-Ameur, W., Gourdin, E., Tolla, P.: Optimal shortest path routing for Internet networks. In: Proceedings of the 1st International Network Optimization Conference (INOC 2003), Paris, France, pp. 119–125 (2003)

  13. 13.

    Boyd, E.: Polyhedral results for the precedence-constrained knapsack problem. Discrete Appl. Math. 41, 185–2001 (1993)

  14. 14.

    Broström, P., Holmberg, K.: Determining the non-existence of compatible OSPF weights. In: Yuan, D. (ed.) Nordic MPS 2004, no. 14 in Linköping Electronic Conference Proceedings, pp. 7–21. Linköping University Electronic Press, Linköping (2004)

  15. 15.

    Broström, P., Holmberg, K.: Valid cycles: A source of infeasibility in OSPF routing. Networks 52, 206–215 (2008)

  16. 16.

    Buriol, L., Resende, M., Ribeiro, C., Thorup, M.: A hybrid genetic algorithm for the weight setting problem in OSPF/IS-IS routing. Networks 46, 36–56 (2005)

  17. 17.

    Callon, R.: Use of OSI IS-IS for routing in TCP/IP and dual environments. IETF Internet RFC 1195 (1990)

  18. 18.

    Ericsson, M., Resende, M., Pardalos, P.: A genetic algorithm for the weight setting problem in OSPF routing. J. Comb. Optim. 6, 299–333 (2002)

  19. 19.

    Fortz, B., Thorup, M.: Increasing Internet capacity using local search. Comput. Optim. Appl. 29, 13–48 (2004)

  20. 20.

    de Giovanni, L., Fortz, B., Labbé, M.: A lower bound for the Internet protocol network design problem. In: Proceedings of the 2nd International Network Optimization Conference (INOC 2005), Lisbon, Portugal, pp. 402–408 (2005)

  21. 21.

    Holmberg, K., Yuan, D.: Optimization of Internet protocol network design and routing. Networks 43, 39–53 (2004)

  22. 22.

    ILOG CPLEX 12.1 (2009). http://ilog.com/products/cplex/

  23. 23.

    LEDA: Library of Efficient Data Types and Algorithms (1998–2003). http://www.algorithmic-solutions.com

  24. 24.

    van de Leensel, R., van Hoesel, C., van de Klundert, J.: Lifting valid inequalities for the precedence constrained knapsack problem. Math. Program. 86, 161–186 (1999)

  25. 25.

    Moy, J.: OSPF version 2. IETF Internet RFC 2328 (1998)

  26. 26.

    Orlowski, S., Pióro, M., Tomaszewski, A., Wessäly, R.: SNDlib 1.0–survivable network design library. Networks (2009). doi:10.1002/net.20371. Preprint version available as ZIB report ZR-07-15

  27. 27.

    Park, K., Park, S.: Lifting cover inequalities for the precedence-constrained knapsack problem. Discrete Appl. Math. 72, 219–241 (1997)

  28. 28.

    Parmar, A., Ahmed, S., Sokol, J.: An integer programming approach to the OSPF weight setting problem. Optimization Online (2006)

  29. 29.

    Pioro, M., Medhi, D.: Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann, San Mateo (2004)

  30. 30.

    Pióro, M., Szentesi, A., Harmatos, J., Jüttner, A.: On OSPF related network optimization problems. In: 8th IFIP Workshop on Performance Modelling and Evaluation of ATM & IP Networks, pp. 70/1–70/14, Ilkley, UK (2000)

  31. 31.

    Prytz, M.: On optimization in design of telecommunications networks with multicast and unicast traffic. Ph.D. thesis, Royal Institute of Technology, Stockholm, Sweden (2002)

  32. 32.

    Tomaszewski, A., Pióro, M., Dzida, M., Mycek, M., Zagożdżon, M.: Valid inequalities for a shortest-path routing optimization problem. In: Proceedings of the 3rd International Network Optimization Conference (INOC 2007), Spa, Belgium (2007)

  33. 33.

    Tomaszewski, A., Pióro, M., Dzida, M., Zagożdżon, M.: Optimization of administrative weights in IP networks using the branch-and-cut approach. In: Proceedings of the 2nd International Network Optimization Conference (INOC 2005), Lisbon, Portugal, pp. 393–400 (2005)

  34. 34.

    Ümit, H., Fortz, B.: Fast heuristic techniques for intra-domain routing metric optimization. In: Proceedings of the 3rd International Network Optimization Conference (INOC 2007), Spa, Belgium (2007)

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Author information

Correspondence to Andreas Bley.

Additional information

This work has been supported by the DFG Research Center Matheon “Mathematics for key technologies” in Berlin.

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Bley, A. An Integer Programming Algorithm for Routing Optimization in IP Networks. Algorithmica 60, 21–45 (2011). https://doi.org/10.1007/s00453-009-9381-5

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  • Shortest path routing
  • Integer programming