Maximum Throughput Network Routing Subject to Fair Flow Allocation

  • Edoardo Amaldi
  • Stefano Coniglio
  • Leonardo TaccariEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8596)


We investigate a bilevel network routing problem where, given a directed graph with a capacity for each arc and a set of elastic traffic demands specified by the corresponding origin-destination pairs, the network operator has to select a single path for each pair so as to maximize the total throughput while assuming that the flows are allocated over the chosen paths according to a fairness principle. We consider max-min fair flow allocation as well as maximum bottleneck flow allocation. After presenting a complexity result, we discuss MILP formulations for the two problem versions, describe a Branch-and-Price algorithm and report some computational results.


Networks Routing Fairness Computational complexity Integer programming 


  1. 1.
    Allalouf, M., Shavitt, Y.: Maximum flow routing with weighted max-min fairness. In: Solé-Pareta, J., Smirnov, M., Van Mieghem, P., Domingo-Pascual, J., Monteiro, E., Reichl, P., Stiller, B., Gibbens, R.J. (eds.) QofIS 2004. LNCS, vol. 3266, pp. 278–287. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  2. 2.
    Amaldi, E., Capone, A., Coniglio, S., Gianoli, L.G.: Network optimization problems subject to max-min fair flow allocation. IEEE Commun. Lett. 17(7), 1463–1466 (2013)CrossRefGoogle Scholar
  3. 3.
    Amaldi, E., Coniglio, S., Gianoli, L.G., Ileri, C.U.: On single-path network routing subject to max-min fair flow allocation. Electron. Notes Discrete Math. 41, 543–550 (2013)CrossRefGoogle Scholar
  4. 4.
    Andrews, M., Chuzhoy, J., Guruswami, V., Khanna, S., Talwar, K., Zhang, L.: Inapproximability of edge-disjoint paths and low congestion routing on undirected graphs. Combinatorica 30(5), 485–520 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Bertsekas, D., Gallager, R.: Data Networks. Prentice-Hall, Upper Saddle River (1992)zbMATHGoogle Scholar
  6. 6.
    Danna, E., Hassidim, A., Kaplan, H., Kumar, A., Mansour, Y., Raz, D., Segalov, M.: Upward max min fairness. In: Proceedings IEEE INFOCOM 2012, pp. 837–845, March 2012Google Scholar
  7. 7.
    Danna, E., Mandal, S., Singh, A.: A practical algorithm for balancing the max-min fairness and throughput objectives in traffic engineering. In: Proceedings IEEE INFOCOM 2012, pp. 846–854, March 2012Google Scholar
  8. 8.
    Fortune, S., Hopcroft, J., Wyllie, J.: The directed subgraph homeomorphism problem. Theor. Comput. Sci. 10(2), 111–121 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Harks, T., Hoefer, M., Schewior, K., Skopalik, A.: Routing games with progressive filling. CoRR abs/1308.3161, abs/1308.3161 (2013)Google Scholar
  10. 10.
    Kleinberg, J., Rabani, Y., Tardos, É.: Fairness in routing and load balancing. In: 40th Annual Symposium on Foundations of Computer Science (FOCS), pp. 568–578. IEEE (1999)Google Scholar
  11. 11.
    Massoulié, L., Roberts, J.: Bandwidth sharing: objectives and algorithms. IEEE/ACM Trans. Netw. 10(3), 320–328 (2002)CrossRefGoogle Scholar
  12. 12.
    Megiddo, N.: Optimal flows in networks with multiple sources and sinks. Math. Program. 7(1), 97–107 (1974)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Nace, D., Pióro, M.: Max-min fairness and its applications to routing and load-balancing in communication networks: a tutorial. Commun. Surv. Tutorials 10(4), 5–17 (2008)Google Scholar
  14. 14.
    Nace, D., Doan, N.L., Klopfenstein, O., Bashllari, A.: Max-min fairness in multi-commodity flows. Comput. Oper. Res. 35(2), 557–573 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Nilsson, P.: Fairness in communication and computer network design. Ph.D. thesis, Lund University, Sweden (2006)Google Scholar
  16. 16.
    Orlowski, S., Wessäly, R., Pióro, M., Tomaszewski, A.: SNDlib 1.0 - survivable network design library. Networks 55(3), 276–286 (2010)Google Scholar
  17. 17.
    Pioro, M.: Fair routing and related optimization problems. In: International Conference on Advanced Computing and Communications (ADCOM), pp. 229–235. IEEE (2007)Google Scholar
  18. 18.
    Radunovic, B., Boudec, J.Y.L.: A unified framework for max-min and min-max fairness with applications. IEEE/ACM Trans. Netw. 15(5), 1073–1083 (2007)CrossRefGoogle Scholar
  19. 19.
    Salles, R.M., Barria, J.A.: Lexicographic maximin optimisation for fair bandwidth allocation in computer networks. Eur. J. Oper. Res. 185(2), 778–794 (2008)CrossRefzbMATHGoogle Scholar
  20. 20.
    Tomaszewski, A.: A polynomial algorithm for solving a general max-min fairness problem. Eur. Trans. Telecommun. 16(3), 233–240 (2005)CrossRefGoogle Scholar
  21. 21.
    Wong, R.: Integer programming formulations of the travelling salesman problem. In: Proceedings IEEE Conference on Circuits and Computers, pp. 149–152 (1980)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Edoardo Amaldi
    • 1
  • Stefano Coniglio
    • 2
  • Leonardo Taccari
    • 1
    Email author
  1. 1.Dipartimento di Elettronica, Informazione e BioingegneriaPolitecnico di MilanoMilanItaly
  2. 2.Lehrstuhl II Für MathematikRWTH Aachen UniversityAachenGermany

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