Abstract
For a directed graph, a Minimum Weight Arborescence (MWA) rooted at a vertex r is a directed spanning tree rooted at r with the minimum total weight. We define the MinArborescence constraint to solve constrained arborescence problems (CAP) in Constraint Programming (CP). A filtering based on the LP reduced costs requires \(O(|V|^2)\) where |V| is the number of vertices. We propose a procedure to strengthen the quality of the LP reduced costs in some cases, also running in \(O(|V|^2)\). Computational results on a variant of CAP show that the additional filtering provided by the constraint reduces the size of the search tree substantially.
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A strong component of a graph G is a maximal (with respect to set inclusion) vertex set \(S \subseteq V\) such that (i) \(|S| = 1\) or (ii) for each pair of distinct vertices i and j in S, at least one path exists in G from vertex i to vertex j [9].
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Houndji, V.R., Schaus, P., Hounkonnou, M.N., Wolsey, L. (2017). The Weighted Arborescence Constraint. In: Salvagnin, D., Lombardi, M. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017. Lecture Notes in Computer Science(), vol 10335. Springer, Cham. https://doi.org/10.1007/978-3-319-59776-8_15
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DOI: https://doi.org/10.1007/978-3-319-59776-8_15
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