The complexity of constraint satisfaction : an algebraic approach.

  title={The complexity of constraint satisfaction : an algebraic approach.},
  author={Andrei A. Krokhin and Andrei A. Bulatov and Peter Jeavons},
Many computational problems arising in artificial intelligence, computer science and elsewhere can be represented as constraint satisfaction and optimization problems. In this survey paper we discuss an algebraic approach that has proved to be very successful in studying the complexity of constraint problems. 

Logic Column 17: A Rendezvous of Logic, Complexity, and Algebra

This article surveys recent advances in applying algebraic techniques to constraint satisfaction problems and suggests a number of novel approaches to solving these problems.

A rendezvous of logic, complexity, and algebra

This article gives a self-contained, contemporary presentation of Schaefer's theorem on Boolean constraint satisfaction, the inaugural result of this area, as well as analogs of this theorem for quantified formulas.

Constraint Satisfaction Problems over the Integers with Successor

This work says that every distance CSP is in P or NP-complete, unless it can be formulated as a finite domain CSP in which case the computational complexity is not known in general.

Relatively quantified constraint satisfaction

This paper gives a complete complexity classification of the cases of the RQCSP where the types of constraints that may appear are specified by a constraint language.

The Computational Complexity of Quantified Constraint Satisfaction

This dissertation investigates the computational complexity of cases of the QCSP where the types of constraints that may appear are restricted and introduces a new concept for proving QCSP tractability results called collapsibility.

The complexity of soft constraint satisfaction

The complexity of temporal constraint satisfaction problems

This work presents a complete complexity classification of the constraint satisfaction problem (CSP) for temporal constraint languages: if the constraint language is contained in one out of nine temporal constraint language, then the CSP can be solved in polynomial time; otherwise, the C SP is NP-complete.

Caterpillar Duality for Constraint Satisfaction Problems

This work considers constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog - monadic linear Datalogs with at most one EDB per rule, and gives combinatorial and algebraic characterisations of such problems, in terms of caterpillar dualities and lattice operations, respectively.

There are no pure relational width 2 constraint satisfaction problems

The Complexity of the Homomorphism Problem for Boolean structures

It is shown that for a fixed Boolean structure $\mathscr B$ of arbitrary finite signature, the problem of deciding whether there exists a homomorphism to $B$ is either in P or NP-complete.



Optimal satisfiability for propositional calculi and constraint satisfaction problems

Foundations of constraint satisfaction

  • E. Tsang
  • Computer Science
    Computation in cognitive science
  • 1993
Introduction to the CSP CSP solving - an overview chapter fundamental concepts of the CSP chapter problem reduction chapter basic search strategies for solving CSPs search orders in searching in CSPs

Complexity classifications of Boolean constraint satisfaction problems

Theorems for Optimization Problems and the Complexity of the Meta-Problems are discussed, as well as some examples of how classification theorems can be applied to optimization problems.

Constraint Satisfaction Problems and Finite Algebras

It is shown that any restricted set of constraint types can be associated with a finite universal algebra and the result is a dichotomy theorem which significantly generalises Schaefer's dichotomy for the Generalised Satisfiability problem.

Programming with Constraints: An Introduction

Part 1 Constraints: constraints simplifications, optimization and implication finite constraint domains, and other constraint programming languages.

A new tractable class of constraint satisfaction problems

  • V. Dalmau
  • Mathematics, Computer Science
    Annals of Mathematics and Artificial Intelligence
  • 2005
A new class of problems called para-primal problems, incomparable with the families identified by Feder and Vardi (1998), is introduced and it is proved that any constraint problem in this class is decidable in polynomial time.

Partial Constraint Satisfaction

The Complexity of Computing the Permanent

  • L. Valiant
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1979