Abstract
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 finite 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(edn) 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 efficient 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 3 d). The special case of linear inequalities can be made arc consistent in time O(en 2 d) using bounds-consistency which exploits special properties of the projection function.
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Yuanlin, Z., Yap, R.H.C. (2000). Arc Consistency on n-ary Monotonic and Linear Constraints. In: Dechter, R. (eds) Principles and Practice of Constraint Programming – CP 2000. CP 2000. Lecture Notes in Computer Science, vol 1894. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45349-0_34
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DOI: https://doi.org/10.1007/3-540-45349-0_34
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