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1 ACRO LIF - Laboratoire d-informatique Fondamentale de Marseille, IBM ILOG CPLEX Madrid 2 LIF - Laboratoire d-informatique Fondamentale de Marseille 3 ACRO - Algorithmique, combinatoire et recherche opérationnelle LIF - Laboratoire d-informatique Fondamentale de Marseille : ACRO

Abstract : Given a network and a set of source destination pairs connections, we con- sider the problem of maximizing the sum of the flow under proportional delay constraints. In this paper, the delay for crossing a link is proportional to the total flow crossing this link. If a connection supports non-zero flow, then the sum of the delay along any path corresponding to that connection must be lower than a given bound. The constraints of delay are on-off constraints because if a connection does not support non-zero flow, then there is no constraint for that connection. The difficulty of the problem comes from the choice of the connections supporting non-zero flow. We first prove a general approximation ratio using linear programming for a variant of the problem. We then prove a Polynomial Time Approximation Scheme when the graph of intersection of the paths has bounded treewidth. We finally prove that the problem is NP-hard even when the network is a tree.

Keywords : Maximum flow on-off delay constraints polynomial time approximation scheme PTAS dynamic programming bounded treewidth linear programming NP-hardness

Autor: Pierre Bonami - Dorian Mazauric - Yann Vaxès -



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