A Hybrid Tractable Class for Non-binary CSPs

Find new islands of tractability, that is classes of CSPs for which polytime algorithms exist, is a fundamental task in the study of constraint satisfaction problems. The concept of hybrid tractable class, which allows to deal simultaneously with the restrictions of languages and, for example, the satisfaction of structural properties, is an approach which has already shown its interest in this domain. Here we study a hybrid class for non-binary CSPs. With this aim in view, we consider the tractable class BTP introduced in [1].While this class has been defined for binary CSPs, the authors have suggested to extend it to CSPs with constraints of arbitrary arities, using the dual representation of such CSPs. We develop this idea by proposing a new definition without exploiting the dual representation, but using a semantic property associated to the compatibility relations of the constraints. This class, called DBTP for Dual BTP, is firstly shown to be tractable. Then it is compared to some known classes. In particular, we prove that DBTP is incomparable with BTP and that it includes some well known classes of CSPs such as beta-acyclic CSPs.

[1]  Bernard A. Nadel,et al.  Tree search and ARC consistency in constraint satisfaction algorithms , 1988 .

[2]  Philippe Jégou,et al.  On the Consistency of General Constraint-Satisfaction Problems , 1993, AAAI.

[3]  David Duris,et al.  Some characterizations of γ and β-acyclicity of hypergraphs , 2012, Inf. Process. Lett..

[4]  Paul D. Seymour,et al.  Graph Minors. II. Algorithmic Aspects of Tree-Width , 1986, J. Algorithms.

[5]  Eugene C. Freuder,et al.  Contradicting Conventional Wisdom in Constraint Satisfaction , 1994, ECAI.

[6]  Philippe Jégou,et al.  Hidden Tractable Classes: From Theory to Practice , 2014, 2014 IEEE 26th International Conference on Tools with Artificial Intelligence.

[7]  Toby Walsh,et al.  Handbook of Constraint Programming , 2006, Handbook of Constraint Programming.

[8]  Fanica Gavril,et al.  Algorithms for Minimum Coloring, Maximum Clique, Minimum Covering by Cliques, and Maximum Independent Set of a Chordal Graph , 1972, SIAM J. Comput..

[9]  Ronald Fagin,et al.  Degrees of acyclicity for hypergraphs and relational database schemes , 1983, JACM.

[10]  Toby Walsh,et al.  Domain filtering consistencies for non-binary constraints , 2008, Artif. Intell..

[11]  Peter van Beek,et al.  On the minimality and global consistency of row-convex constraint networks , 1995, JACM.

[12]  Catriel Beeri,et al.  On the Desirability of Acyclic Database Schemes , 1983, JACM.

[13]  Martin C. Cooper,et al.  On Guaranteeing Polynomially Bounded Search Tree Size , 2011, International Conference on Principles and Practice of Constraint Programming.

[14]  Eugene C. Freuder.  A Sufficient Condition for Backtrack-Free Search , 1982, JACM.

[15]  M. Golumbic.  Algorithmic graph theory and perfect graphs , 1980 .

[16]  Martin C. Cooper,et al.  Characterising Tractable Constraints , 1994, Artif. Intell..

[17]  David A. Cohen,et al.  A New Classs of Binary CSPs for which Arc-Constistency Is a Decision Procedure , 2003, CP.

[18]  Martin C. Cooper,et al.  Tractable Constraints on Ordered Domains , 1995, Artif. Intell..

[19]  Peter Jeavons,et al.  Perfect Constraints Are Tractable , 2008, CP.

[20]  Philippe Jégou,et al.  A filtering process for general constraint-satisfaction problems: achieving pairwise-consistency using an associated binary representation , 1989, [Proceedings 1989] IEEE International Workshop on Tools for Artificial Intelligence.

[21]  Philippe Jégou.  Decomposition of Domains Based on the Micro-Structure of Finite Constraint-Satisfaction Problems , 1993, AAAI.

[22]  Philippe Jégou.  Contribution à l'étude des problèmes de satisfaction de contraintes : algorithmes de propagation et de résolution : propagation de contraintes dans les réseaux dynamiques , 1991 .

[23]  Martin C. Cooper,et al.  Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination , 2010, Artif. Intell..

[24]  Philippe Jégou,et al.  Some New Tractable Classes of CSPs and Their Relations with Backtracking Algorithms , 2013, CPAIOR.