Abstract
Constructive methods obtain solutions to constraint satisfaction problem instances by iteratively extending consistent partial assignments. In this research, we study the solution paths in the search space of constructive methods and examine their distribution among the assignments of the search space. By properly employing the entropy of this distribution, we derive measures of the average amount of choice available within the search space for constructing a solution. The derived quantities directly reflect both the number and the distribution of solutions, an ”open question” in the phase transition literature. We show that constrainedness, an acknowledged predictor of computational cost, is an aggregate measure of choice deficit. This establishes a connection between an algorithm-independent property of the search space, such as the inherent choice available for constructing a solution, and the algorithm-dependent amount of resources required to actually construct a solution.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Williams, C., Hogg, T.: Exploiting the deep structure of constraint problems. Artificial Intellingence 70, 73–117 (1994)
Shannon, C.E.: A mathematical theory of communication. The Bell Systems Technical Journal 27 (1948), Reprinted with corrections
Crutchfield, J., Feldman, D.: Regularities unseen, randomness observed: Levels of entropy convergence. Chaos 13, 25–54 (2003)
Gent, I.P., MacIntyre, E., Prosser, P., Walsh, T.: The constrainedness of search. In: AAAI/IAAI, vol. 1, pp. 246–252 (1996)
Gent, I.P., MacIntyre, E., Prosser, P., Walsh, T.: The constrainedness of arc consistency. In: Principles and Practice of Constraint Programming, pp. 327–340 (1997)
Walsh, T.: The constrainedness knife-edge. In: AAAI/IAAI, pp. 406–411 (1998)
Ornstein, D.: Bernoulli shifts with the same entropy are isomorphic. Adv. Math. 4, 337–352 (1970)
Slaney, J.: Is there a constrainedness knife-edge? In: Proceedings of the 14th European Conference on Artificial Intelligence, pp. 614–618 (2000)
Hogg, T.: Refining the phase transitions in combinatorial search. Artificial Intelligence 81, 127–154 (1996)
Parkes, A.J.: Clustering at the phase transition. In: AAAI/IAAI, pp. 340–345 (1997)
Hogg, T., Huberman, B., Williams, C.: Phase transitions and the search problem. Artificial Intelligence 81, 1–15 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Boukeas, G., Stamatopoulos, P., Halatsis, C., Zissimopoulos, V. (2004). Inherent Choice in the Search Space of Constraint Satisfaction Problem Instances. In: Vouros, G.A., Panayiotopoulos, T. (eds) Methods and Applications of Artificial Intelligence. SETN 2004. Lecture Notes in Computer Science(), vol 3025. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24674-9_38
Download citation
DOI: https://doi.org/10.1007/978-3-540-24674-9_38
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21937-8
Online ISBN: 978-3-540-24674-9
eBook Packages: Springer Book Archive