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Article Dans Une Revue Discrete Applied Mathematics Année : 2014

Fractional routing using pairs of failure-disjoint paths

Résumé

Given a set of commodities and a network where some arcs can fail while others are reliable, we consider a routing problem with respect to a survivability requirement that each commodity can be split among pairs of failure-disjoint paths. Two paths pp and p′p′ form a pair of failure-disjoint paths if they share only reliable arcs. The same flow is sent over pp and p′p′, but the flow sent on a common reliable arc is not doubled. We present a compact linear formulation of the problem. Also three non-compact formulations solvable by column generation are introduced. In the first formulation, the generated columns correspond to pairs of failure-disjoint paths, while in the second formulation the generated columns correspond to simple paths. The third formulation is solved by generating pairs of arc-disjoint paths. All formulations are compared numerically. On top of that we study some generalizations and some special cases of the problem of computing a shortest pair of failure-disjoint paths. One of these generalizations is equivalent to a single-commodity capacitated network design problem

Dates et versions

hal-01263061 , version 1 (27-01-2016)

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Walid Ben-Ameur, Michal Pioro, Mateusz Zotkiewicz. Fractional routing using pairs of failure-disjoint paths. Discrete Applied Mathematics, 2014, 164 (1), pp.47 - 60. ⟨10.1016/j.dam.2011.12.019⟩. ⟨hal-01263061⟩
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