Abstract
We study the experimental consequences of a recent theoretical result by Achlioptas et al. that shows that conventional models of random problems are trivially insoluble in the limit. We survey the literature to identify experimental studies that lie within the scope of this result. We then estimate theoretically and measure experimentally the size at which problems start to become trivially insoluble. Our results demonstrate that most (but not all) of these experimental studies are luckily unaffected by this result. We also study an alternative model of random problems that does not suffer from this asymptotic weakness. We show that, at a typical problem size used in experimental studies, this model looks similar to conventional models. Finally, we generalize this model so that we can independently adjust the constraint tightness and density
Supported by EPSRC awards GR/L/24014 and GR/K/65706. The authors wish to thank other members of the APES research group. We are especially grateful to Ian Gent who derived the expected number of cliques in a random graph
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
D. Achlioptas, L.M. Kirousis, E. Kranakis, D. Krizanc, M.S.O. Molloy, and C. Stamatiou. Random constraint satisfaction: A more accurate picture. In Proceedings of Third International Conference on Principles and Practice of Constraint Programming (CP97), pages 107–120, 1997.
P. Cheeseman, B. Kanefsky, and W.M. Taylor. Where the really hard problems are. In Proceedings of the 12th IJCAI, pages 331–337. International Joint Conference on Artificial Intelligence, 1991.
E. Friedgut. Sharp thresholds for graph properties and the k-SAT problem, 1998. Unpublished manuscrip.
A. Frieze and S. Suen. Analysis of two simple heuristics on a random instance of k-SAT. Journal of Algorithms, 20:312–355, 1996.
I.P. Gent, E. MacIntyre, P. Prosser, P. Shaw, and T. Walsh. The constrainedness of arc consistency. In 3rd International Conference on Principles and Practices of Constraint Programming (CP-97), pages 327–340. Springer, 1997.
I.P. Gent, E. MacIntyre, P. Prosser, B.M. Smith, and T. Walsh. An empirical study of dynamic variable ordering heuristics for the constraint satisfaction problem. In 2nd International Conference on Principles and Practices of Constraint Programming (CP-96), pages 179–193, 1996.
I.P. Gent, E. MacIntyre, P. Prosser, and T. Walsh. Scaling effects in the CSP phase transition. In 1st International Conference on Principles and Practices of Constraint Programming (CP-95), pages 70–87. Springer-Verlag, 1995.
I.P. Gent, E. MacIntyre, P. Prosser, and T. Walsh. The constrainedness of search. In Proceedings of the 13th National Conference on AI, pages 246–252. American Association for Artificial Intelligence, 1996.
I.P. Gent, E. MacIntyre, P. Prosser, and T. Walsh. The scaling of search cost. In Proceedings of the 14th National Conference on AI, pages 315–320. American Association for Artificial Intelligence, 1997.
I.P. Gent and T. Walsh. Phase transitions from real computational problems. In Proceedings of the 8th International Symposium on Artificial Intelligence, pages 356–364, 1995.
C. Gomes and B. Selman. Problem structure in the presence of perturbations. In Proceedings of the 14th National Conference on AI, pages 221–226. American Association for Artificial Intelligence, 1997.
S. Grant and B.M. Smith. The phase transition behaviour of maintaining arc consistency. Research Report 95.25 School of Computer Studies University of Leeds1995. A revised and shortened version appears in Proceedings of 12th ECAI, pages 175–179, 1996.
L.M. Kirousis, E. Kranakis, and D. Krizanc. Approximating the unsatisfiability threshold of random formulas. In Proceedings of the 4th Annual European Symposium on Algorithms (ESA’96), pages 27–38, 1996.
D. Mitchell, B. Selman, and H. Levesque. Hard and Easy Distributions of SAT Problems. In Proceedings of the 10th National Conference on AI, pages 459–465. American Association for Artificial Intelligence, 1992.
C. Williams and T. Hogg. Exploiting the deep structure of constraint problems. Artificial Intelligence, 70:73–117, 1994.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
MacIntyre, E., Prosser, P., Smith, B., Walsh, T. (1998). Random Constraint Satisfaction: theory meets practice. In: Maher, M., Puget, JF. (eds) Principles and Practice of Constraint Programming — CP98. CP 1998. Lecture Notes in Computer Science, vol 1520. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49481-2_24
Download citation
DOI: https://doi.org/10.1007/3-540-49481-2_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-65224-3
Online ISBN: 978-3-540-49481-2
eBook Packages: Springer Book Archive