Complexity Analysis of Heuristic CSP Search Algorithms

CSP search algorithms are exponential in the worst-case. A trivial upper bound on the time complexity of CSP search algorithms is O∗ (dn ), where n and d are the number of variables and the maximal domain size of the underlying CSP, respectively. In this paper we show that a combination of heuristic methods of constraint solving can reduce the time complexity. In particular, we prove that the FC-CBJ algorithm combined with the fail-first variable ordering heuristic (FF) achieves time complexity of O∗ ((d − 1)n ), where n and d are the number of variables and the maximal domain size of the given CSP, respectively. Furthermore, we show that the combination is essential because neither FC-CBJ alone nor FC with FF achieve the above complexity. The proposed results are interesting because they establish connection between theoretical and practical approaches to CSP research.

• Type: Conference
• Year: 2005
• Where: CSCLP
• Authors: Igor Razgon
• Keywords: CSCLP 2005, CSP Search Algorithms, Maximal Domain Size, Time Complexity