Exploiting the constrainedness in constraint satisfaction problems

Nowadays, many real problem in Artificial Intelligence can be modeled as constraint satisfaction problems (CSPs). A general rule in constraint satisfaction is to tackle the hardest part of a search problem first. In this paper, we introduce a parameter (tau) that measures the constrainedness of a search problem. This parameter represents the probability of the problem being feasible. A value of tau = 0 corresponds to an over-constrained problem and no states are expected to be solutions. A value of tau = 1 corresponds to an under-constrained problem which every state is a solution. This parameter can also be used in a heuristic to guide search. To achieve this parameter, a sample in finite population is carried out to compute the tightnesses of each constraint. We take advantage of this tightnesses to classify the constraints from the tightest constraint to the loosest constraint. This heuristic may accelerate the search due to inconsistencies can be found earlier and the number of constraint checks can significantly be reduced.