Designing Steiner networks with unicyclic connected components : an easy problem

Abstract : This paper focuses on the design of minimum-cost networks satisfying two technical constraints. First, the connected components should be unicyclic. Second, some given special nodes must belong to cycles. This problem is a generalization of two known problems: the perfect binary 2-matching problem and the problem of computing a minimum-weight basis of the bicircular matroid. It turns out that the problem is polynomially solvable. An exact extended linear formulation is provided. We also present a partial description of the convex hull of the incidence vectors of these Steiner networks. Polynomial-time separation algorithms are described. One of them is a generalization of the Padberg-Rao algorithm to separate blossom inequalities
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Journal articles
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https://hal.archives-ouvertes.fr/hal-01308332
Contributor : Médiathèque Télécom Sudparis & Institut Mines-Télécom Business School <>
Submitted on : Wednesday, April 27, 2016 - 3:44:04 PM
Last modification on : Wednesday, January 15, 2020 - 12:36:08 PM

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Walid Ben-Ameur, Makhlouf Hadji. Designing Steiner networks with unicyclic connected components : an easy problem. SIAM Journal on Discrete Mathematics, Society for Industrial and Applied Mathematics, 2010, 24 (4), pp.1541 - 1557. ⟨10.1137/090759033⟩. ⟨hal-01308332⟩

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