Improved bounds on the complexity of kB-consistency

Authors:
Lucas Bordeaux;Eric Monfroy;Frédéric Benhamou
Affiliations:
IRIN, Université de Nantes, France;IRIN, Université de Nantes, France;IRIN, Université de Nantes, France
Venue:
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Year:
2001

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Abstract

kB-consistencies form the class of strong consistencies used in interval constraint programming. We survey, prove, and give theoretical motivations to some technical improvements to a naive kB- consistency algorithm. Our contribution is twofold: on the one hand, we introduce an optimal 3B- consistency algorithm whose time-complexity of O(md2n) improves the known bound by a factor n (m is the number of constraints, n is the number of variables, and d is the maximal size of the intervals of the box). On the other hand, we prove that improved bounds on time complexity can effectively be reached for higher values of k. These results are obtained with very affordable overheads in terms of space complexity.