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Journal Articles European Journal of Operational Research Year : 2008

Simple Bounds and Greedy Algorithms for Decomposing a Flow into a Minimal Set of Paths

Bénédicte Vatinlen
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Fabrice Chauvet
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Philippe Chrétienne
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Philippe Mahey

Abstract

Given arbitrary source and target nodes s, t and an s–t-flow defined by its flow-values on each arc of a network, we consider the problem of finding a decomposition of this flow with a minimal number of s–t-paths. This problem is issued from the engineering of telecommunications networks for which the task of implementing a routing solution consists in integrating a set of end-to-end paths. We show that this problem is NP-hard in the strong sense and give some properties of an optimal solution. We then propose upper and lower bounds for the number of paths in an optimal solution. Finally we develop two heuristics based on the properties of a special set of solutions called saturating solutions.

Dates and versions

hal-01185177 , version 1 (19-08-2015)

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Cite

Bénédicte Vatinlen, Fabrice Chauvet, Philippe Chrétienne, Philippe Mahey. Simple Bounds and Greedy Algorithms for Decomposing a Flow into a Minimal Set of Paths. European Journal of Operational Research, 2008, 185 (3), pp.1390-1401. ⟨10.1016/j.ejor.2006.05.043⟩. ⟨hal-01185177⟩
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