On the edge capacitated Steiner tree problem

Abstract : Given a graph G = (V, E) with a root r ∈ V , positive capacities {c(e)|e ∈ E}, and non-negative lengths {(e)|e ∈ E}, the minimum-length (rooted) edge capacitated Steiner tree problem is to find a tree in G of minimum total length, rooted at r, spanning a given subset T ⊂ V of vertices, and such that, for each e ∈ E, there are at most c(e) paths, linking r to vertices in T , that contain e. We study the complexity and approximability of the problem, considering several relevant parameters such as the number of terminals, the edge lengths and the minimum and maximum edge capacities. For all but one combinations of assumptions regarding these parameters, we settle the question, giving a complete characterization that separates tractable cases from hard ones. The only remaining open case is proved to be equivalent to a long-standing open problem. We also prove close relations between our problem and classical Steiner tree as well as vertex-disjoint paths problems.
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Pré-publication, Document de travail
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Contributeur : Marie-Christine Costa <>
Soumis le : dimanche 12 février 2017 - 09:49:51
Dernière modification le : samedi 9 février 2019 - 01:23:48
Document(s) archivé(s) le : samedi 13 mai 2017 - 12:28:31


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  • HAL Id : hal-01465403, version 1
  • ARXIV : 1607.07082


Cédric Bentz, Marie-Christine Costa, Alain Hertz. On the edge capacitated Steiner tree problem. 2017. 〈hal-01465403〉



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