Abstract
This article presents an arc-consistency algorithm for the tree constraint, which enforces the partitioning of a digraph \(\mathcal{G}\) = (\(\mathcal{V},\mathcal{E}\)) into a set of vertex-disjoint anti-arborescences. It provides a necessary and sufficient condition for checking the tree constraint in \(\mathcal{O}(|\mathcal{V}| + |\mathcal{E}|)\) time, as well as a complete filtering algorithm taking \(\mathcal{O}(|\mathcal{V}| \cdot |\mathcal{E}|)\) time.
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Beldiceanu, N., Flener, P., Lorca, X. (2005). The tree Constraint. In: Barták, R., Milano, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2005. Lecture Notes in Computer Science, vol 3524. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11493853_7
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DOI: https://doi.org/10.1007/11493853_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26152-0
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