Abstract
Our goal is to investigate the definition and application of strong consistency properties on the dual graphs of binary Constraint Satisfaction Problems (CSPs). As a first step in that direction, we study the structure of the dual graph of binary CSPs, and show how it can be arranged in a triangle-shaped grid. We then study, in this context, Relational Neighborhood Inverse Consistency (RNIC), which is a consistency property that we had introduced for non-binary CSPs [17]. We discuss how the structure of the dual graph of binary CSPs affects the consistency level enforced by RNIC. Then, we compare, both theoretically and empirically, RNIC to Neighborhood Inverse Consistency (NIC) and strong Conservative Dual Consistency (sCDC), which are higher-level consistency properties useful for solving difficult problem instances. We show that all three properties are pairwise incomparable.
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References
Bacchus, F., Chen, X., Beek, P.V., Walsh, T.: Binary vs. Non-Binary Constraints. Artificial Intelligence 140, 1–37 (2002)
Bessière, C.: Constraint Propagation. In: Handbook of Constraint Programming. Elsevier (2006)
Debruyne, R., Bessière, C.: From Restricted Path Consistency to Max-Restricted Path Consistency. In: Smolka, G. (ed.) CP 1997. LNCS, vol. 1330, pp. 312–326. Springer, Heidelberg (1997)
Debruyne, R., Bessière, C.: Some Practicable Filtering Techniques for the Constraint Satisfaction Problem. In: Proceedings of the 15th International Joint Conference on Artificial Intelligence, pp. 412–417 (1997)
Debruyne, R., Bessière, C.: Domain Filtering Consistencies. Journal of Artificial Intelligence Research 14, 205–230 (2001)
Dechter, R.: Constraint Processing. Morgan Kaufmann (2003)
Freuder, E.C.: A Sufficient Condition for Backtrack-Free Search. JACM 29(1), 24–32 (1982)
Freuder, E.C., Elfe, C.D.: Neighborhood Inverse Consistency Preprocessing. In: Proceedings of AAAI 1996, Portland, Oregon, pp. 202–208 (1996)
Golumbic, M.C.: Algorithmic Graph Theory and Perfect Graphs. Annals of Discrete Mathematics, vol. 75. Elsevier (2004)
Janssen, P., Jégou, P., Nougier, B., Vilarem, M.C.: A Filtering Process for General Constraint-Satisfaction Problems: Achieving Pairwise-Consistency Using an Associated Binary Representation. In: IEEE Workshop on Tools for AI, pp. 420–427 (1989)
Karakashian, S., Woodward, R., Reeson, C., Choueiry, B.Y., Bessière, C.: A First Practical Algorithm for High Levels of Relational Consistency. In: 24th AAAI Conference on Artificial Intelligence (AAAI 2010), pp. 101–107 (2010)
Kjærulff, U.: Triagulation of Graphs - Algorithms Giving Small Total State Space. Research Report R-90-09, Aalborg University, Denmark (1990)
Lecoutre, C., Cardon, S., Vion, J.: Conservative Dual Consistency. In: Proceedings of AAAI 2007, pp. 237–242 (2007)
Lecoutre, C., Cardon, S., Vion, J.: Second-Order Consistencies. Journal of Artificial Intelligence Research 40, 175–219 (2011)
Mackworth, A.K.: Consistency in Networks of Relations. Artificial Intelligence 8, 99–118 (1977)
Sabin, D., Freuder, E.C.: Contradicting Conventional Wisdom in Constraint Satisfaction. In: Proceedings of the 11th European Conference on Artificial Intelligence, Amsterdam, The Netherlands, pp. 125–129 (1994)
Woodward, R., Karakashian, S., Choueiry, B.Y., Bessière, C.: Solving Difficult CSPs with Relational Neighborhood Inverse Consistency. In: 25th AAAI Conference on Artificial Intelligence (AAAI 2011), pp. 112–119 (2011)
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Woodward, R.J., Karakashian, S., Choueiry, B.Y., Bessiere, C. (2012). Revisiting Neighborhood Inverse Consistency on Binary CSPs. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_50
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DOI: https://doi.org/10.1007/978-3-642-33558-7_50
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