Abstract
The k-consistency algorithm for constraint-satisfaction problems proceeds, roughly, by finding all partial solutions on at most k variables and iteratively deleting those that cannot be extended to a partial solution by one more variable. It is known that if the core of the structure encoding the scopes of the constraints has treewidth at most k, then the k-consistency algorithm is always correct. We prove the exact converse to this: if the core of the structure encoding the scopes of the constraints does not have treewidth at most k, then the k-consistency algorithm is not always correct. This characterizes the exact power of the k-consistency algorithm in structural terms.
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Atserias, A., Bulatov, A., Dalmau, V. (2007). On the Power of k-Consistency. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds) Automata, Languages and Programming. ICALP 2007. Lecture Notes in Computer Science, vol 4596. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73420-8_26
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DOI: https://doi.org/10.1007/978-3-540-73420-8_26
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