Measures of Intrinsic Hardness for Constraint Satisfaction Problem Instances

Our aim is to investigate the factors which determine the intrinsic hardness of constructing a solution to any particular constraint satisfaction problem instance, regardless of the algorithm employed. The line of reasoning is roughly the following: There exists a set of distinct, possibly overlapping, trajectories through the states of the search space, which start at the unique initial state and terminate at complete feasible assignments. These trajectories are named solution paths. The entropy of the distribution of solution paths among the states of each level of the search space provides a measure of the amount of choice available for selecting a solution path at that level. This measure of choice is named solution path diversity. Intrinsic instance hardness is identified with the deficit in solution path diversity and is shown to be linked to the distribution of instance solutions as well as constrainedness, an established hardness measure.