Simpler and Incremental Consistency Checking and Arc Consistency Filtering Algorithms for the Weighted Spanning Tree Constraint

The weighted spanning tree contraint is defined from a set of variables X and a value K. The variables X represent the nodes of a graph and the domain of a variable x ∈ X the neighbors of the node in the graph. In addition each pair (variable, value) is associated with a cost. This constraint states that the graph defined from the variables and the domains of the variables admits a spanning tree whose cost is less than K. Efficient algorithms to compute a minimum spanning tree or to establish arc consistency of this constraint have been proposed. However, these algorithms are based on complex procedures that are rather difficult to understand and to implement. In this paper, we propose and detail simpler algorithms for checking the consistency of the constraint and for establishing arc consistency. In addition, we propose for the first time incremental algorithms for this constraint, that is algorithms that have been designed in order to be efficiently maintained during the search for solution.