PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A New Tractable Class of Constraint Satisfaction Problems
Victor Dalmau
Annals of Mathematics and Artificial Intelligence Volume 44, Number 1-2, pp. 61-85, 2005.


In this paper we consider constraint satisfaction problems where the set of constraint relations is fixed. Feder and Vardi (1998) identified three families of constraint satisfaction problems containing all known polynomially solvable problems. We introduce a new class of problems called {\em para-primal} problems, incomparable with the families identified by Feder and Vardi (1998) and we prove that any constraint problem in this class is decidable in polynomial time. As an application of this result we prove a complete classification for the complexity of constraint satisfaction problems under the assumption that the basis contains all the permutation relations. In the proofs, we make an intensive use of algebraic results from clone theory about the structure of para-primal and homogeneous algebras.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:1833
Deposited By:Victor Dalmau
Deposited On:29 November 2005