Abstract
In many real-world settings, e.g. product configuration, constraint satisfaction problems are compiled into automata or binary decision diagrams, which can be seen as instances of Darwiche’s negation normal form. In this paper we consider settings in which a foreground set of constraints can be added to a set of consistent background constraints, that are compactly represented in a compiled form. When the set of foreground constraints introduces inconsistencies with the background constraints we wish to find relaxations of the problem by identifying the subset of the foreground constraints that do not introduce inconsistency; such a subset is called a relaxation. This paper is organised in two parts. First, two novel algorithms for finding relaxations based on automata are presented. They find the relaxation that is consistent with the largest (or smallest) number of solutions from amongst the longest ones (first algorithm), or from amongst the set-wise maximal ones (second algorithm). Then, we generalise our results by identifying the properties that the target compilation language must have for our approach to apply. Finally, we show empirically that on average our algorithms can be more than 500 times faster than a current state-of-the-art algorithm.
This work was supported by Science Foundation Ireland (Grant No. 05/IN/I886).
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.
References
Amilhastre, J., Fargier, H., Marguis, P.: Consistency restoration and explanations in dynamic CSPs – application to configuration. Artif. Intell. 135, 199–234 (2002)
Bailey, J., Stuckey, P.J.: Discovery of minimal unsatisfiable subsets of constraints using hitting set dualization. In: Hermenegildo, M.V., Cabeza, D. (eds.) PADL 2004. LNCS, vol. 3350, pp. 174–186. Springer, Heidelberg (2005)
Bowen, J.: Using dependency records to generate design coordination advice in a constraint-based approach to concurrent engineering. Computers in Industry 22(1), 191–199 (1997)
Darwiche, A.: Decomposable negation normal form. J. ACM 48(4), 608–647 (2001)
Darwiche, A.: On the tractable counting of theory models and its application to truth maintenance and belief revision. Journal of Applied Non-Classical Logics 11(1-2), 11–34 (2001)
Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Res (JAIR) 17, 229–264 (2002)
Freuder, E.C., Likitvivatanavong, C., Moretti, M., Rossi, F., Wallace, R.J.: Computing explanations and implications in preference-based configurators. In: O’Sullivan, B. (ed.) CologNet 2002. LNCS (LNAI), vol. 2627, pp. 76–92. Springer, Heidelberg (2003)
Friedrich, G.: Elimination of spurious explanations. In: Proceedings of ECAI, pp. 813–817 (2004)
Gregoire, E., Mazure, B., Piette, C.: Boosting a complete technique to find mss and mus thanks for a local search oracle. In: Proceedings of IJCAI, pp. 2300–2305 (2007)
Junker, U.: QuickXplain: preferred explanations and relaxations for over-constrained problems. In: Proceedings of AAAI, pp. 167–172 (2004)
Liffiton, M.H., Moffitt, M.D., Pollack, M.E., Sakallah, K.A.: Identifying conflicts in overconstrained temporal problems. In: Kaelbling, L.P., Saffiotti, A. (eds.) IJCAI, pp. 205–211. Professional Book Center (2005)
Liffiton, M.H., Sakallah, K.A.: On finding all minimally unsatisfiable subformulas. In: Bacchus, F., Walsh, T. (eds.) SAT 2005. LNCS, vol. 3569, pp. 173–186. Springer, Heidelberg (2005)
O’Callaghan, B., O’Sullivan, B., Freuder, E.C.: Generating corrective explanations for interactive constraint satisfaction. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 445–459. Springer, Heidelberg (2005)
O’Sullivan, B., Papadopoulos, A., Faltings, B., Pu, P.: Representative explanations for over-constrained problems. In: AAAI, pp. 323–328 (2007)
Pu, P., Faltings, B., Torrens, M.: Effective interaction principles for online product search environments. Web Intelligence, 724–727 (2004)
Sqalli, M.H., Freuder, E.C.: Inference-based constraint satisfaction supports explanation. In: Proceedings of AAAI, pp. 318–325 (1996)
Vempaty, N.R.: Solving constraint satisfaction problems using finite state automata. In: AAAI, pp. 453–458 (1992)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Papadopoulos, A., O’Sullivan, B. (2008). Relaxations for Compiled Over-Constrained Problems. 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_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-85958-1_29
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)