Solving minimum-cost shared arborescence problems

Eduardo Álvarez-Miranda 1 Ivana Ljubić 2 Martin Luipersbeck 3 Markus Sinnl 4
4 INOCS - Integrated Optimization with Complex Structure
ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this work, we consider the minimum-cost shared Steiner arborescence problem (SStA). In this problem, the goal is to find a minimum-cost subgraph, which is shared among multiple entities and each entity is able to establish a cost-efficient Steiner arborescence. The SStA has been recently used in the literature to establish shared functional modules in protein-protein interaction networks. We propose a cut-based formulation for the problem, and design two exact algorithmic approaches: one based on the separation of connectivity cut inequalities, and the other corresponding to a Benders decomposition of the former model. Both approaches are enhanced by various techniques, including (i) preprocessing, (ii) stabilized cut generation, (iii) primal heuristics, and (iv) cut management. These two algorithmic alternatives are computationally evaluated and compared with a previously proposed flow-based formulation. We illustrate the effectiveness of the algorithms on two types of instances derived from protein-protein interaction networks (available from the previous literature) and from telecommunication access networks.
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Journal articles
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https://hal.inria.fr/hal-01666315
Contributor : Markus Sinnl <>
Submitted on : Monday, December 18, 2017 - 11:14:41 AM
Last modification on : Friday, March 22, 2019 - 1:34:16 AM

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Eduardo Álvarez-Miranda, Ivana Ljubić, Martin Luipersbeck, Markus Sinnl. Solving minimum-cost shared arborescence problems. European Journal of Operational Research, Elsevier, 2017, 258 (3), pp.887 - 901. ⟨10.1016/j.ejor.2016.11.004⟩. ⟨hal-01666315⟩

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