# Asking the Metaquestions in Constraint Tractability

@article{Chen2017AskingTM,
title={Asking the Metaquestions in Constraint Tractability},
author={Hubie Chen and Beno{\^i}t Larose},
journal={ACM Trans. Comput. Theory},
year={2017},
volume={9},
pages={11:1-11:27}
}
• Published 4 April 2016
• Computer Science
• ACM Trans. Comput. Theory
The constraint satisfaction problem (CSP) involves deciding, given a set of variables and a set of constraints on the variables, whether or not there is an assignment to the variables satisfying all of the constraints. One formulation of the CSP is as the problem of deciding, given a pair (G ℍ) of relational structures, whether or not there is a homomorphism from the first structure to the second structure. The CSP is generally NP-hard; a common way to restrict this problem is to fix the second…

## Figures and Tables from this paper

Algebraic approach to promise constraint satisfaction
• Computer Science
STOC
• 2019
A new class of problems that can be viewed as algebraic versions of the (Gap) Label Cover problem are introduced, and it is shown that every PCSP with a fixed constraint language is equivalent to a problem of this form.
A dichotomy theorem for nonuniform CSPs simplified
The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language G the problem CSP(G) is either solvable in polynomial time or is NP-complete.
A Dichotomy Theorem for Nonuniform CSPs
• A. Bulatov
• Mathematics
2017 IEEE 58th Annual Symposium on Foundations of Computer Science (FOCS)
• 2017
The Dichotomy Conjecture for the non-uniform CSP states that for every constraint language \Gm the problem CSP is either solvable in polynomial time or is NP-complete.
The Constraint Satisfaction Problem: Complexity and Approximability
• Computer Science
The Constraint Satisfaction Problem
• 2017
This report documents the material presented during the course of the Dagstuhl Seminar 18231 “The Constraint Satisfaction Problem: Complexity and Approximability”, aimed at bringing together researchers using all the different techniques in the study of the CSP to share their insights obtained.
Testing the complexity of a valued CSP language
It is proved that for any constant $\delta<1$ there is no $O(\sqrt[3]{3}^{\,\delta|D|})$ algorithm, assuming that SETH holds, and a matching lower bound under the Strong Exponential Time Hypothesis is obtained.
Harnessing tractability in constraint satisfaction problems
This thesis attempts to bridge the gap between practitioners and theorists of CSP by providing polynomial-time algorithms to test for membership in a selection of major tractable classes, and proposes a general framework to adapt the concept of kernelization, central to parameterized complexity but hitherto rarely used in practice, to the context of constraint reasoning.
The Smallest Hard Trees
• Computer Science
• 2022
It is proved that for every orientation of a tree with fewer vertices the corresponding CSP can be solved in polynomial time, and a method to generate orientations of trees that are cores that works well in practice is presented.
Testability of Homomorphism Inadmissibility: Property Testing Meets Database Theory
• Mathematics, Computer Science
PODS
• 2019
The characterization shows that homomorphism inadmissibility from A is constant-query testable with one-sided error if and only if the core of A is alpha-acyclic; this result generalizes existing results for testing subgraph-freeness in the general graph model.
The Dichotomy for Conservative Constraint Satisfaction is Polynomially Decidable
The main contribution of this paper is a polynomial-time algorithm that, given a constraint language $$\varGamma$$ as input, decides if c-CSP($$\var Gamma$$) is tractable.

## References

SHOWING 1-10 OF 57 REFERENCES
(Smart) Look-Ahead Arc Consistency and the Pursuit of CSP Tractability
• Computer Science
CP
• 2004
This paper introduces a new approach to obtaining CSP(B) tractability results: instead of starting with a class of structures, it starts with an algorithm called look-ahead arc consistency, and gives an algebraic characterization of the structures solvable by the algorithm.
Complexity of conservative constraint satisfaction problems
This work completely characterize conservative constraint languages that give rise to polynomial time solvable CSP classes, and obtains a complete description of those (directed) graphs H for which the List H-Coloring problem is solvable in polynometric time.
Domain permutation reduction for constraint satisfaction problems
• Computer Science, Mathematics
Artif. Intell.
• 2008
Quantified Constraint Satisfaction and the Polynomially Generated Powers Property
This article identifies a new combinatorial property on algebras, the polynomially generated powers (PGP) property, which it is shown is tightly connected to QCSP complexity, and introduces another new property, switchability, which both implies the PGP property and implies positive complexity results on the QCSP.
Meditations on Quantified Constraint Satisfaction
A viewpoint on the research program of understanding the complexity of the problems QCSP( B ) on finite structures is offered and a group of conjectures are proposed and discussed.
The complexity of satisfiability problems
An infinite class of satisfiability problems is considered which contains these two particular problems as special cases, and it is shown that every member of this class is either polynomial-time decidable or NP-complete.
Classifying the Complexity of Constraints Using Finite Algebras
• Mathematics
SIAM J. Comput.
• 2005
It is shown that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra is explored.
Universal Algebra and Hardness Results for Constraint Satisfaction Problems
• Mathematics, Computer Science
ICALP
• 2007
Algebraic conditions on constraint languages Γ are presented that ensure the hardness of the constraint satisfaction problem CSP(Γ) for complexity classes L, NL, P, NP and ModpL and it is shown that if C SP( Γ) is not first-order definable then it is L-hard.
Tractable Structures for Constraint Satisfaction with Truth Tables
• D. Marx
• Computer Science
Theory of Computing Systems
• 2009
A new hypergraph measure adaptive width is introduced and it is shown that CSP with truth tables is polynomial-time solvable if restricted to a class of hypergraphs with bounded adaptive width.