On the Subexponential Time Complexity of CSP

Iyad Kanj; Stefan Szeider

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arXiv · 1304.1996

On the Subexponential Time Complexity of CSP

Iyad Kanj·Stefan Szeider

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Abstract

A CSP with n variables ranging over a domain of d values can be solved by brute-force in d^n steps (omitting a polynomial factor). With a more careful approach, this trivial upper bound can be improved for certain natural restrictions of the CSP. In this paper we establish theoretical limits to such improvements, and draw a detailed landscape of the subexponential-time complexity of CSP. We first establish relations between the subexponential-time complexity of CSP and that of other problems, including CNF-Sat. We exploit this connection to provide tight characterizations of the subexponential-time complexity of CSP under common assumptions in complexity theory. For several natural CSP parameters, we obtain threshold functions that precisely dictate the subexponential-time complexity of CSP with respect to the parameters under consideration. Our analysis provides fundamental results indicating whether and when one can significantly improve on the brute-force search approach for solving CSP.

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Iyad Kanj, Stefan Szeider. 2013-04-07. On the Subexponential Time Complexity of CSP. https://arxiv.org/abs/1304.1996

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