An Empirical Investigation of Value Ordering for Finding All Solutions

Traditional backtracking search algorithms for solving constraint satisfaction problems select a variable and then construct a separate branch for each value in the variable’s domain: the order in which the values are assigned then has no effect on the overall search, when finding all solutions. Constraint solvers such as ILOG Solver and ECLPS instead use binary branching in constructing search trees: each node represents a choice between assigning a value to a variable and not assigning that value. The value ordering does then affect the search effort when finding all solutions. We show how this can happen by analysing search trees formed under opposite value orders and investigate empirically the effect on search from different value orders. The mechanism by which a good value order can prune the search suggests what we should aim for in choosing a value order. We suggest that for some classes of problem, lexicographic order may still be a priori a reasonable choice.