# The complexity of constraint satisfaction : an algebraic approach.

@inproceedings{Krokhin2005TheCO, title={The complexity of constraint satisfaction : an algebraic approach.}, author={Andrei A. Krokhin and Andrei A. Bulatov and Peter Jeavons}, year={2005} }

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.

## 48 Citations

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

- MathematicsArXiv
- 2006

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

- MathematicsCSUR
- 2009

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

- Computer Science, MathematicsICALP
- 2015

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

- BusinessConstraints
- 2008

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

- Computer Science
- 2004

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 temporal constraint satisfaction problems

- Computer ScienceJACM
- 2010

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

- Mathematics2008 23rd Annual IEEE Symposium on Logic in Computer Science
- 2008

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

- MathematicsInf. Process. Lett.
- 2009

### The Complexity of the Homomorphism Problem for Boolean structures

- MathematicsArXiv
- 2020

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.

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