Arc Consistency on n-ary Monotonic and Linear Constraints

Many problems and applications can be naturally modelled and solved using constraints with more than two variables Such n ary constraints in particular arithmetic constraints are provided by many nite domain constraint programming systems The best known worst case time complexity of existing algorithms GAC schema for enforcing arc consistency on general CSPs is O ed where d is the size of domain e is the number of constraints and n is the maximum number of variables in a single constraint We address the question of e cient consistency enforcing for n ary constraints An observation here is that even with a restriction of n ary constraints to linear constraints arc consistency enforcing is NP complete We identify a general class of monotonic n ary constraints which includes linear inequalities as a special case Such monotonic constraints can be made arc consistent in time O en d The special case of linear inequalities can be made arc consistent in time O en d using bounds consistency which exploits special properties of the projection function