A CSP with n variables ranging over a domain of d values can be solved by brute-force in dn 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.
Para más detalles puedes leer al paper.