Max-Min fair distribution of modular network flows on fixed paths

Authors:
Pål Nilsson;Michał Pióro
Affiliations:
Department of Communication Systems, Lund University, Sweden, Lund, Sweden;Department of Communication Systems, Lund University, Sweden, Lund, Sweden
Venue:
NETWORKING'06 Proceedings of the 5th international IFIP-TC6 conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communications Systems
Year:
2006

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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.