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Journal Articles Theoretical Computer Science Year : 2017

Maximum flow under proportional delay constraint

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Abstract

Given a network and a set of source destination pairs (connections), we consider 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 delays 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 carries 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 linear time 2-approximation algorithm when the network is a path. We finally show a Polynomial Time Approximation Scheme when the graph of intersections of the paths has bounded treewidth.
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Dates and versions

hal-01571232 , version 1 (01-08-2017)

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Pierre Bonami, Dorian Mazauric, Yann Vaxès. Maximum flow under proportional delay constraint. Theoretical Computer Science, 2017, 689, pp.58-66. ⟨10.1016/j.tcs.2017.05.034⟩. ⟨hal-01571232⟩
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