Constraint Tightness versus Global Consistency

Constraint networks are a simple represen tation and reasoning framework with diverse applications In this paper we present a new property called constraint tightness that can be used for characterizing the di culty of problems formulated as constraint networks Speci cally we show that when the con straints are tight they may require less pre processing in order to guarantee a backtrack free solution This suggests for example that many instances of crossword puzzles are relatively easy while scheduling problems in volving resource constraints are quite hard Formally we present a relationship between the tightness or restrictiveness of the con straints and the level of local consistency su cient to ensure global consistency thus ensuring backtrack freeness Two de nitions of local consistency are employed The tradi tional variable based notion leads to a con dition involving the tightness of the con straints the level of local consistency and the arity of the constraints while a new de nition of relational consistency leads to a condition expressed in terms of tightness and local consistency level alone New al gorithms for enforcing relational consistency are introduced and analyzed