Strong Domain Filtering Consistencies for Non-Binary Constraint Satisfaction Problems

Abstract

Domain filtering local consistencies, such as inverse consistencies, that only delete values and do not add new constraints are particularly useful in Constraint Programming. Although many such consistencies for binary constraints have been proposed and evaluated, the situation with non-binary constraints is quite different. Only very recently have domain filtering consistencies stronger than GAC started to attract interest. Following this line of research, we define a number of strong domain filtering consistencies for non-binary constraints and theoretically compare their pruning power. We prove that three of these consistencies are equivalent to maxRPC in binary CSPs while another is equivalent to PIC. We also describe a generic algorithm for domain filtering consistencies in non-binary CSPs. We show how this algorithm can be instantiated to enforce some of the proposed consistencies and analyze the worst-case complexities of the resulting algorithms. Finally, we make a preliminary empirical study.

A new branch-and-filter exact algorithm for binary constraint satisfaction problems

“…Finally, another interesting and very challenging line of research concerns the extension of Bfilt+ for general CSPs. As mentioned in the introduction, different binarization strategies have been proposed in the literature to solve CSPs of greater arity than two as a BCSP, see Dechter & Pearl (1989) ; Rossi et al (1990) ; Stergiou & Walsh (1999) . A future line of work is the characterization of those nonbinary constraints and binarization methods for which a clique based algorithm would be efficient, and the extension of Bfilt+ for these non-binary problems.…”

“…It is worth mentioning that any CSP can be transformed into a BCSP via a reduction called binarization . This reduction can be performed in different ways, and we refer the interested reader to Rossi, Petrie, & Dhar (1990) ; Samaras & Stergiou (2005) ; Stergiou & Walsh (1999) . All the binarization techniques have typically the negative effects of increasing the number of variables and/or the size of the variable domains.…”

Encoding Constraints as Binary Constraint Networks Satisfying BTP

“…(Dechter 1990) showed that the expressiveness of BCNs can be significantly improved with hidden variables. In addition, various binary encodings with hidden variables have been proposed to encode table constraints (Yap, Xia, and Wang 2020) as BCNs, such as the dual encoding (Dechter and Pearl 1989), hidden variable encoding (Rossi, Petrie, and Dhar 1990), double encoding (Stergiou and Walsh 1999) and bipartite encoding (Wang and Yap 2020). Although all constraint relations can be represented as table constraints, the tabulation of constraints may cause exponential blowup.…”