Abstract
Constraint Programming is a powerful approach for modeling and solving many combinatorial problems, scalability, however, remains an issue in practice. Abstraction and reformulation techniques are often sought to overcome the complexity barrier. In this paper we introduce four reformulation techniques that operate on the various components of a Constraint Satisfaction Problem (CSP) in order to reduce the cost of problem solving and facilitate scalability. Our reformulations modify one or more component of the CSP (i.e., the query, variables domains, constraints) and detect symmetrical solutions to avoid generating them. We describe each of these reformulations in the context of CSPs, then evaluate their performance and effects in on the building identification problem introduced by Michalowski and Knoblock [1].
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
Michalowski, M., Knoblock, C.: A Constraint Satisfaction Approach to Geospatial Reasoning. In: Proc. of AAAI 2005, pp. 423–429 (2005)
Choueiry, B.Y., Iwasaki, Y., McIlraith, S.: Towards a Practical Theory of Reformulation for Reasoning About Physical Systems. Artificial Intelligence 162 (1–2), 145–204 (2005)
Giunchiglia, F., Walsh, T.: A Theory of Abstraction. Artificial Intelligence 57(2-3), 323–389 (1992)
Dechter, R., van Beek, P.: Local and global relational consistency. Journal of Theoretical Computer Science (1996)
Dechter, R.: Constraint Processing. Morgan Kaufmann, San Francisco (2003)
Russell, S., Norvig, P.: Artificial Intelligence: A Modern Approach. In: Artificial Intelligence: A Modern Approach, p. 107. Prentice-Hall, Englewood Cliffs (2003)
Selman, B., Kautz, H.: Knowledge Compilation and Theory Approximation. Journal of the ACM 43(2), 193–224 (1996)
Milano, M.: Constraint and Integer Programming: Toward a Unified Methodology. Kluwer, Dordrecht (2004)
Ellman, T.: Abstraction via Approximate Symmetry. In: IJCAI 1993, pp. 916–921 (1993)
Régin, J.: A filtering algorithm for constraints of difference in csps. In: AAAI 1994, pp. 362–367 (1994)
Uno, T.: Algorithms for Enumerating All Perfect, Maximum and Maximal Matchings in Bipartite Graphs. In: Leong, H.-V., Jain, S., Imai, H. (eds.) ISAAC 1997. LNCS, vol. 1350, pp. 92–101. Springer, Heidelberg (1997)
Berge, C.: Graphs and Hypergraphs. Elsevier, Amsterdam (1973)
West, D.: Introduction to Graph Theory, 2nd edn. Prentice-Hall, Englewood Cliffs (2001)
Hopcroft, J.E., Karp, R.M.: An n 5/2 Algorithm for Maximum Matchings in Bipartite Graphs. SIAM 2, 225–231 (1973)
Bessière, C., Meseguer, P., Freuder, E., Larrosa, J.: On Forward Checking for Non-binary Constraint Satisfaction. In: Jaffar, J. (ed.) Principles and Practice of Constraint Programming – CP 1999. LNCS, vol. 1713, pp. 88–102. Springer, Heidelberg (1999)
Prosser, P.: MAC-CBJ: Maintaining Arc Consistency with Conflict-Directed Backjumping. Technical Report 95/177, Univ. of Strathclyde (1995)
Nadel, B.: Representation Selection for Constraint Satisfaction: A Case Study Using n-Queens. IEEE Expert 5(3), 16–24 (1990)
Glaisher, J.: On the Problem of the Eight Queens. Philosophical Magazine 4(48), 457–467 (1874)
Puget, J.: On the satisfiability of symmetrical constraint satisfaction problems. In: Komorowski, J., Raś, Z.W. (eds.) ISMIS 1993. LNCS, vol. 689, pp. 350–361. Springer, Heidelberg (1993)
Holte, R.C., Choueiry, B.Y.: Abstraction and Reformulation in Artificial Intelligence. Philosophical Trans. of the Royal Society Sec. Biological Sciences 358(1435), 1197–1204 (2003)
Razgon, I., O’Sullivan, B., Provan, G.: Generalizing Global Constraints Based on Network Flows. In: Workshop on Constraint Modelling and Reformulation, pp. 74–87 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bayer, K.M., Michalowski, M., Choueiry, B.Y., Knoblock, C.A. (2007). Reformulating Constraint Satisfaction Problems to Improve Scalability. In: Miguel, I., Ruml, W. (eds) Abstraction, Reformulation, and Approximation. SARA 2007. Lecture Notes in Computer Science(), vol 4612. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73580-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-73580-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73579-3
Online ISBN: 978-3-540-73580-9
eBook Packages: Computer ScienceComputer Science (R0)