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Solving minimum-cost shared arborescence problems. (English) Zbl 1394.90429
Summary: 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.

MSC:
90C10 Integer programming
90C35 Programming involving graphs or networks
90B10 Deterministic network models in operations research
90C11 Mixed integer programming
90C57 Polyhedral combinatorics, branch-and-bound, branch-and-cut
Software:
OGDF; SteinLib
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