Abstract
In this paper a new aspect of the classical max-min fairness fixed-path problem is investigated. The considered (multi-criteria) optimization problem is almost identical to the continuous-flow problem, with the additional complicating assumption that flows must be integral. We show that such an extension makes the problem substantially more difficult (in fact \({\mathcal NP}\)-hard). Through comparison with the closely related continuous-flow problem, a number of properties for the solution of the extended problem are derived. An algorithm, based on sequential resolution of linear programs, that shows to be useful (produce optimal solutions) for many instances of the considered problem, is given. It follows that this algorithm can be made exact, through substituting the involved linear programs by mixed-integer programs.
Chapter PDF
Similar content being viewed by others
References
Bertsekas, D., Gallager, R.: Data Networks. Prentice Hall, Englewood Cliffs (1987)
Nace, D.: A linear programming based approach for computing optimal fair splittable routing. In: IEEE International Symposium on Computers and Communications, pp. 468–474 (2002)
Pióro, M., Nilsson, P., Kubilinskas, E., Fodor, G.: On efficient max-min fair routing algorithms. In: IEEE International Symposium on Computers and Communications, pp. 465–472 (2003)
Pióro, M., Medhi, D.: Routing, Flow, and Capacity Design in Communication and Computer Networks. Morgan Kaufmann (Elsevier), San Francisco (2004)
Kleinberg, J., Rabani, Y., Tardos, E.: Fairness in routing and load balancing. Journal of Computer and System Sciences 63(1), 2–20 (2001)
Nilsson, P., Pióro, M.: Unsplittable max-min demand allocation – a routing problem. In: HETNETs 2005, p. 26 (2005)
Garey, M., Johnson, D.: Computers and intractability – a guide to the theory of NP-completeness. Freeman, New York (1979)
Nilsson, P.: Some simple special cases of FIXMMF-MF. Technical report, Dept. of Communication Sytems, Lund University (2005)
Ogryczak, W., Pioro, M., Tomaszewski, A.: Telecommunications network design and max-min optimization problem. Journal of telecommunications and information technology 3 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 IFIP International Federation for Information Processing
About this paper
Cite this paper
Nilsson, P., Pióro, M. (2006). Max-Min Fair Distribution of Modular Network Flows on Fixed Paths. In: Boavida, F., Plagemann, T., Stiller, B., Westphal, C., Monteiro, E. (eds) NETWORKING 2006. Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communications Systems. NETWORKING 2006. Lecture Notes in Computer Science, vol 3976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753810_76
Download citation
DOI: https://doi.org/10.1007/11753810_76
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34192-5
Online ISBN: 978-3-540-34193-2
eBook Packages: Computer ScienceComputer Science (R0)