Abstract
The tightness of a constraint refers to how restricted the constraint is. The existing work shows that there exists a relationship between tightness and global consistency of a constraint network. In this paper, we conduct a comprehensive study on this relationship. Under the concept of k-consistency (k is a number), we strengthen the existing results by establishing that only some of the tightest, not all, binary constraints are used to predict a number k such that strong k-consistency ensures global consistency of an arbitrary constraint network which may include non-binary constraints. More importantly, we have identified a lower bound of the number of the tightest constraints we have to consider in predicting the number k. To make better use of the tightness of constraints, we propose a new type of consistency: dually adaptive consistency. Under this concept, only the tightest directionally relevant constraint on each variable (and thus in total n–1 such constraints where n is the number of variables) will be used to predict the level of “consistency” ensuring global consistency of a network.
This work has received support from Science Foundation Ireland under Grant 00/PI.1/C075.
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© 2004 Springer-Verlag Berlin Heidelberg
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Zhang, Y. (2004). On Tightness of Constraints. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_65
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DOI: https://doi.org/10.1007/978-3-540-30201-8_65
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23241-4
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