A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
The range and roots constraints: specifying counting and occurrence problems
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
CPAIOR'05 Proceedings of the Second international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
The "Not-Too-Heavy Spanning Tree" Constraint
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Graph properties based filtering
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
The minimum spanning tree constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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We present two constraints that partition the vertices of an undirected n-vertex, m-edge graph ${\mathcal{G}}=({\mathcal{V}},{\mathcal{E}})$ into a set of vertex-disjoint trees. The first is the resource-forest constraint, where we assume that a subset ${\mathtt{R}}\subseteq {\mathcal{V}}$ of the vertices are resource vertices. The constraint specifies that each tree in the forest must contain at least one resource vertex. This is the natural undirected counterpart of the tree constraint [1], which partitions a directed graph into a forest of directed trees where only certain vertices can be tree roots. We describe a hybrid-Consistency algorithm that runs in ${\mathop{\cal O}}(m+n)$ time for the resource forest constraint, a sharp improvement over the ${\mathop{\cal O}}(mn)$ bound that is known for the directed case. The second constraint is proper-forest. In this variant, we do not have the requirement that each tree contains a resource, but the forest must contain only proper trees, i.e., trees that have at least two vertices each. We develop a hybrid-Consistency algorithm for this case whose running time is ${\mathop{\cal O}}(mn)$ in the worst case, and ${\mathop{\cal O}}(m\sqrt{n})$ in many (typical) cases.