A Dichotomy for 2-Constraint Forbidden CSP Patterns

Novel tractable classes of the binary CSP (constraint satisfaction problem) have recently been discovered by studying classes of instances defined by excluding subproblems described by patterns. The complete characterisation of all tractable classes defined by forbidden patterns is a challenging problem. We demonstrate a dichotomy in the case of forbidden patterns consisting of two constraints.

[1]  Martin C. Cooper,et al.  Hierarchically Nested Convex VCSP , 2011, CP.

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

[3]  Martin Grohe.  The complexity of homomorphism and constraint satisfaction problems seen from the other side , 2007, JACM.

[4]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[5]  Eugene C. Freuder.  Eliminating Interchangeable Values in Constraint Satisfaction Problems , 1991, AAAI.

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

[7]  Andrei A. Bulatov,et al.  A dichotomy theorem for constraint satisfaction problems on a 3-element set , 2006, JACM.

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

[9]  Dániel Marx,et al.  Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries , 2009, JACM.

[10]  Roland H. C. Yap,et al.  An optimal coarse-grained arc consistency algorithm , 2005, Artif. Intell..

[11]  Dániel Marx,et al.  Can you beat treewidth? , 2007, 48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07).

[12]  Martin C. Cooper,et al.  Hybrid tractability of valued constraint problems , 2010, Artif. Intell..

[13]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[14]  Martin C. Cooper.  Fundamental Properties of Neighbourhood Substitution in Constraint Satisfaction Problems , 1997, Artif. Intell..

[15]  Peter Jeavons,et al.  Classifying the Complexity of Constraints Using Finite Algebras , 2005, SIAM J. Comput..