On the Subexponential Time Complexity of CSP
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.
Cite
@article{arxiv.1304.1996,
title = {On the Subexponential Time Complexity of CSP},
author = {Iyad Kanj and Stefan Szeider},
journal= {arXiv preprint arXiv:1304.1996},
year = {2013}
}