Refining Constraint Weighting

Backtracking search is a complete approach that is traditionally used to solve instances modeled as constraint satisfaction problems. The space explored during search depends dramatically on the order that variables are instantiated. Considering that a perfect variable ordering might result to a backtrack-free search (i.e., finding backdoors, cycle cutsets), finding heuristics for variable ordering has always attracted research interest. For fifteen years, constraint weighting has been shown to be a successful approach for guiding backtrack search. In this paper, we show how the popular generic variable ordering heuristic dom/wdeg can be made more robust by taking finer information at each conflict: the "current" arity of the failing constraint as well as the size of the current domains of the variables involved in that constraint. Our experimental results show the practical interest of this refined variant of constraint weighting.