On the Subexponential Time Complexity of CSP

Authors

  • Iyad Kanj DePaul University
  • Stefan Szeider Vienna University of Technology

DOI:

https://doi.org/10.1609/aaai.v27i1.8609

Keywords:

Constraint Satisfaction, Subexponential Time, Exponential Time Hypothesis, Treewidth

Abstract

A Constraint Satisfaction Problem (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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Published

2013-06-30

How to Cite

Kanj, I., & Szeider, S. (2013). On the Subexponential Time Complexity of CSP. Proceedings of the AAAI Conference on Artificial Intelligence, 27(1), 459-465. https://doi.org/10.1609/aaai.v27i1.8609