Abstract
By using recent results from graph theory, including the Strong Perfect Graph Theorem, we obtain a unifying framework for a number of tractable classes of constraint problems. These include problems with chordal microstructure; problems with chordal microstructure complement; problems with tree structure; and the “all-different” constraint. In each of these cases we show that the associated microstructure of the problem is a perfect graph, and hence they are all part of the same larger family of tractable problems.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Chudnovsky, M., Cornuéjols, G., Liu, X., Seymour, P., Vušković, K.: Recognizing Berge graphs. Combinatorica 25(2), 143–186 (2005)
Chudnovsky, M., Robertson, N., Seymour, P., Thomas, R.: The strong perfect graph theorem. Annals of Mathematics 164(1), 51–229 (2006)
Cohen, D.A.: A new class of binary CSPs for which arc-consistency is a decision procedure. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 807–811. Springer, Heidelberg (2003)
Green, M.J., Cohen, D.A.: Domain permutation reduction for constraint satisfaction problems. Artificial Intelligence 172(8–9), 1094–1118 (2008)
Grötschel, M., Lovász, L., Schrijver, A.: The ellipsoid method and its consequences in combinatorial optimization. Combinatorica 1(2), 169–197 (1981)
Hougardy, S.: Classes of perfect graphs. Discrete Math. 306, 2529–2571 (2006)
Jégou, P.: Decomposition of domains based on the micro-structure of finite constraint-satisfaction problems. In: Proceedings AAAI 1993, pp. 731–736 (1993)
Peterson, D.: Gridline graphs: a review in two dimensions and an extension to higher dimensions. Discrete Applied Mathematics 126, 223–239 (2003)
Régin, J.C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings AAAI 1994, pp. 362–367 (1994)
Rossi, F., van Beek, P., Walsh, T. (eds.): Handbook of Constraint Programming. Elsevier, Amsterdam (2006)
Yıldırım, E.A., Fan-Orzechowski, X.: On extracting maximum stable sets in perfect graphs using Lovász’s theta function. Comp. Optim. and Appl. 33, 229–247 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Salamon, A.Z., Jeavons, P.G. (2008). Perfect Constraints Are Tractable. In: Stuckey, P.J. (eds) Principles and Practice of Constraint Programming. CP 2008. Lecture Notes in Computer Science, vol 5202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85958-1_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-85958-1_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85957-4
Online ISBN: 978-3-540-85958-1
eBook Packages: Computer ScienceComputer Science (R0)