The tree Constraint

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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