Understanding and improving the MAC algorithm
Constraint satisfaction problems have wide application in artificial intelligence. They involve finding values for problem variables where the values must be consistent in that they satisfy restrictions on which combinations of values are allowed. Recent research on finite domain constraint satisfaction problems suggest that Maintaining Arc Consistency (MAC) is the most efficient general CSP algorithm for solving large and hard problems. In the first part of this paper we explain why maintaining full, as opposed to limited, arc consistency during search can greatly reduce the search effort. Based on this explanation, in the second part of the paper we show how to modify MAC in order to make it even more efficient. Experimental results prove that the gain in efficiency can be quite important.
Unable to display preview. Download preview PDF.
- 1.Bessiere, C., and Regin, J.-C. 1996. Mac and combined heuristics: Two reasons to forsake fc (and cbj?) on hard problems. In Second International Conference on Principles and Practice of Constraint Programming — CP96, number 1118 in Lecture Notes in Computer Science, 61–75.Google Scholar
- 2.Bessiere, C.; Freuder, E. C.; and Regin, J.-C. 1995. Using inference to reduce arc consistency computation. In Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence, volume I, 592–598.Google Scholar
- 3.Dechter, R., and Pearl, J. 1987. The cycle-cutset method for improving search performance in ai applications. In Proceedings of the 3rd IEEE Conference on AI Applications, 224–230.Google Scholar
- 4.Dechter, R., and Pearl, J. 1988. Network-based heuristics for constraint satisfaction problems. Artificial Intelligence 34(1):1–38.Google Scholar
- 5.Freuder, E. C. 1982. A sufficient condition for backtrack-free search. Journal of the ACM 29(1):24–32.Google Scholar
- 6.Grant, S. A., and Smith, B. M. 1995. The phase transition behaviour of maintaining arc consistency. Technical Report 95.25, University of Leeds, School of Computer Studies.Google Scholar
- 7.Hyvonen, E. 1992. Constraint reasoning based on interval arithmetic: the tolerance propagation approach. Artificial Intelligence 58(1-3):71–112.Google Scholar
- 8.Nadel, B. 1988. Tree search and arc-consistency in constraint satisfaction algorithms. In Kanal, L., and Kumar, V., eds., Search in Artificial Intelligence. Springer-Verlag. 287–342.Google Scholar
- 9.Regin, J.-C. 1995. Developpement d'outils algorithmiques pour l'Intelligence Artilacielle. Application a la chimie organique. Ph.D. Dissertation, Universite Montpellier II.Google Scholar
- 10.Rossi, F. 1995. Redundant Hidden Variables in Finite domain Constraint Problems. In Constraint Processing, number 923 in Lecture Notes in Computer Science, 205–233.Google Scholar
- 11.Sabin, D., and Freuder, E. C. 1994. Contradicting conventional wisdom in constraint satisfaction. In Proceedings of the 11th European Conference on Artificial Intelligence.Google Scholar
- 12.Solotorevsky, G.; Gudes, E.; and Meisels, A. 1996. Modeling and solving distributed constraint satisfaction problems (dcsps). In Second International Conference on Principles and Practice of Constraint Programming — CP96, number 1118 in Lecture Notes in Computer Science, 561–562.Google Scholar