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We study the constraint satisfaction problem (CSP) parameterized by a constraint language (CSP) and how the choice of affects its worst-case time complexity. Under the exponential-time hypothesis (ETH), we rule out the existence of subexponential algorithms for finite-domain NP-complete CSP problems. This extends to certain infinite-domain CSPs and structurally restricted problems. For CSPs with finite domain D and where all unary relations are available, we identify a relation SD such that the time complexity of the NP-complete problem CSP(SD) is a lower bound for all NP-complete CSPs of this kind. We also prove that the time complexity of CSP(SD) strictly decreases when D increases (unless the ETH is false) and provide stronger complexity results in the special case when D=3.
ACM Transactions on Computation Theory (TOCT) – Association for Computing Machinery
Published: Jan 21, 2021
Keywords: Constraint satisfaction problems
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