Abstract
We investigate the parameterized complexity of deciding whether a constraint network is k-consistent. We show that, parameterized by k, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size d and the maximum number l of constraints in which a variable occurs. We show that parameterized by k + d, the problem drops down one complexity level and becomes co-W[1]-complete. Parameterized by k + d + l the problem drops down one more level and becomes fixed-parameter tractable. We further show that the same complexity classification applies to strong k-consistency, directional k-consistency, and strong directional k-consistency.
Our results establish a super-polynomial separation between input size and time complexity. Thus we strengthen the known lower bounds on time complexity of k-consistency that are based on input size.
This research was funded by the ERC (COMPLEX REASON, 239962).
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Gaspers, S., Szeider, S. (2011). The Parameterized Complexity of Local Consistency. In: Lee, J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23786-7_24
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DOI: https://doi.org/10.1007/978-3-642-23786-7_24
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