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 *(d n ), 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.
KeywordsTime Complexity Domain Size Partial Solution Constraint Satisfaction Problem Polynomial Factor
Unable to display preview. Download preview PDF.
- 1.Bacchus, F.: Extending forward checking. In: Principles and Practice of Constraint Programming, pp. 35–51 (2000)Google Scholar
- 3.Eppstein, D.: Improved algorithms for 3-coloring, 3-edge coloring and constraint satisfaction. In: SODA-2001, pp. 329–337 (2001)Google Scholar
- 6.Prosser, P.: MAC-CBJ: maintaining arc consistency with conflict-directed backjumping. Technical Report Research Report/95/177, Dept. of Computer Science, University of Strathclyde (1995)Google Scholar