A sufficient condition for backtrack-bounded search
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Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
Constraint relaxation may be perfect
Artificial Intelligence
From local to global consistency
Artificial Intelligence
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
A generic arc-consistency algorithm and its specializations
Artificial Intelligence
Fast parallel constraint satisfaction
Artificial Intelligence
Monotone monadic SNP and constraint satisfaction
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Decomposing constraint satisfaction problems using database techniques
Artificial Intelligence
Characterising tractable constraints
Artificial Intelligence
Tractable constraints on ordered domains
Artificial Intelligence
A relational model of data for large shared data banks
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A Unifying Framework for Tractable Constraints
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Hypertree decompositions and tractable queries
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Constraint satisfaction and database theory: a tutorial
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Building tractable disjunctive constraints
Journal of the ACM (JACM)
The complexity of maximal constraint languages
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
The complexity of acyclic conjunctive queries
Journal of the ACM (JACM)
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
SIGACT news complexity theory column 34
ACM SIGACT News
Fixed-parameter complexity in AI and nonmonotonic reasoning
Artificial Intelligence
Exploiting structure in quantified formulas
Journal of Algorithms
Constraints and universal algebra
Annals of Mathematics and Artificial Intelligence
Hypertree Decompositions: A Survey
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Satisfiability of Systems of Equations over Finite Monoids
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Constraint Satisfaction Problems and Finite Algebras
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Towards a Predictive Computational Complexity Theory
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Constraint Satisfaction Problems in Non-deterministic Logarithmic Space
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Fixed-Parameter Complexity in AI and Nonmonotonic Reasoning
LPNMR '99 Proceedings of the 5th International Conference on Logic Programming and Nonmonotonic Reasoning
The Complexity of Minimal Satisfiability Problems
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Solving Order Constraints in Logarithmic Space
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Constraint (Logic) Programming: A Survey on Research and Applications
Selected papers from the Joint ERCIM/Compulog Net Workshop on New Trends in Contraints
Learnability of Quantified Formulas
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
CP '98 Proceedings of the 4th International Conference on Principles and Practice of Constraint Programming
New Tractable Classes from Old
CP '02 Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming
Boolean Formulas are Hard to Learn for most Gate Bases
ALT '99 Proceedings of the 10th International Conference on Algorithmic Learning Theory
On Tractable Queries and Constraints
DEXA '99 Proceedings of the 10th International Conference on Database and Expert Systems Applications
Consistency and set intersection
Eighteenth national conference on Artificial intelligence
New tractable constraint classes from old
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New Tractable Classes From Old
Constraints
Learnability of quantified formulas
Theoretical Computer Science
The complexity of minimal satisfiability problems
Information and Computation
SIGACT news complexity theory column 43
ACM SIGACT News
Implementing a Test for Tractability
Constraints
A new tractable class of constraint satisfaction problems
Annals of Mathematics and Artificial Intelligence
Recognizing frozen variables in constraint satisfaction problems
Theoretical Computer Science
The expressive rate of constraints
Annals of Mathematics and Artificial Intelligence
Constraint solving via fractional edge covers
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
The complexity of partition functions
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
H-Coloring dichotomy revisited
Theoretical Computer Science - Graph colorings
The complexity of soft constraint satisfaction
Artificial Intelligence
A rendezvous of logic, complexity, and algebra
ACM SIGACT News
Towards a dichotomy theorem for the counting constraint satisfaction problem
Information and Computation
Domain permutation reduction for constraint satisfaction problems
Artificial Intelligence
On digraph coloring problems and treewidth duality
European Journal of Combinatorics
Majority constraints have bounded pathwidth duality
European Journal of Combinatorics
The complexity of temporal constraint satisfaction problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Graphs, polymorphisms and the complexity of homomorphism problems
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Properties of tree convex constraints
Artificial Intelligence
Computational Complexity of Constraint Satisfaction
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Quantified Positive Temporal Constraints
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
The expressive power of valued constraints: Hierarchies and collapses
Theoretical Computer Science
Tractable Quantified Constraint Satisfaction Problems over Positive Temporal Templates
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Relatively quantified constraint satisfaction
Constraints
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
Complexity of Constraints
Recent Results on the Algebraic Approach to the CSP
Complexity of Constraints
Introduction to the Maximum Solution Problem
Complexity of Constraints
Homogeneous and strictly homogeneous criteria for partial structures
Discrete Applied Mathematics
Existentially restricted quantified constraint satisfaction
Information and Computation
The complexity of satisfiability problems: Refining Schaefer's theorem
Journal of Computer and System Sciences
Affine systems of equations and counting infinitary logic
Theoretical Computer Science
Maximal infinite-valued constraint languages
Theoretical Computer Science
A new line of attack on the dichotomy conjecture
Proceedings of the forty-first annual ACM symposium on Theory of computing
Tricolorable torus knots are NP-complete
Proceedings of the 47th Annual Southeast Regional Conference
Semilinear Program Feasibility
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
A rendezvous of logic, complexity, and algebra
ACM Computing Surveys (CSUR)
The complexity of constraint satisfaction games and QCSP
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Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
Collapsibility and consistency in quantified constraint satisfaction
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Tractable tree convex constraint networks
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Approximability of the Maximum Solution Problem for Certain Families of Algebras
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
Set intersection and consistency in constraint networks
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A comparison of structural CSP decomposition methods
IJCAI'99 Proceedings of the 16th international joint conference on Artifical intelligence - Volume 1
Amalgams of constraint satisfaction problems
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A maximal tractable class of soft constraints
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Constraint satisfaction, databases, and logic
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
A combinatorial constraint satisfaction problem dichotomy classification conjecture
European Journal of Combinatorics
The complexity of quantified constraint satisfaction problems under structural restrictions
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Constraints, consistency and closure
Artificial Intelligence
The complexity of soft constraint satisfaction
Artificial Intelligence
The complexity of temporal constraint satisfaction problems
Journal of the ACM (JACM)
TABLEAUX '09 Proceedings of the 18th International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Approximating fractional hypertree width
ACM Transactions on Algorithms (TALG)
Complexity of default logic on generalized conjunctive queries
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Enumerating all solutions for constraint satisfaction problems
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Generalized modal satisfiability
Journal of Computer and System Sciences
Constraint satisfaction problems and global cardinality constraints
Communications of the ACM
Distance constraint satisfaction problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Congruence Distributivity Implies Bounded Width
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Complexity of conservative constraint satisfaction problems
ACM Transactions on Computational Logic (TOCL)
Proceedings of the forty-third annual ACM symposium on Theory of computing
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
On the CSP dichotomy conjecture
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Constraint satisfaction parameterized by solution size
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
An algebraic theory of complexity for valued constraints: establishing a Galois connection
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The Complexity of Positive First-Order Logic without Equality
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Quantified Equality Constraints
SIAM Journal on Computing
Linear programming, width-1 CSPs, and robust satisfaction
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An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Typed guarded decompositions for constraint satisfaction
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Approximability of integer programming with generalised constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
The complexity of equality constraint languages
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Generalized modal satisfiability
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An algebraic approach to the complexity of generalized conjunctive queries
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Systems of equations over finite semigroups and the #CSP dichotomy conjecture
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Approximability of bounded occurrence max ones
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The core of a countably categorical structure
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Minimization for generalized Boolean formulas
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Survey: Colouring, constraint satisfaction, and complexity
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An efficient algorithm for a class of constraint satisfaction problems
Operations Research Letters
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Maximal infinite-valued constraint languages
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Datalog and constraint satisfaction with infinite templates
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Constraint satisfaction problems: Convexity makes AllDifferent constraints tractable
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Weak near-unanimity functions and digraph homomorphism problems
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The complexity of conservative valued CSPs
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The complexity of finite-valued CSPs
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Qualitative constraint satisfaction problems: An extended framework with landmarks
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The complexity of three-element min-sol and conservative min-cost-hom
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Constraint satisfaction tractability from semi-lattice operations on infinite sets
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Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
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Constraint Satisfaction Problems Solvable by Local Consistency Methods
Journal of the ACM (JACM)
Semilattice polymorphisms and chordal graphs
European Journal of Combinatorics
Why is it Hard to Obtain a Dichotomy for Consistent Query Answering?
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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Many combinatorial search problems can be expressed as “constraint satisfaction problems” and this class of problems is known to be NP-complete in general. In this paper, we investigate the subclasses that arise from restricting the possible constraint types. We first show that any set of constraints that does not give rise to an NP-complete class of problems must satisfy a certain type of algebraic closure condition. We then investigate all the different possible forms of this algebraic closure property, and establish which of these are sufficient to ensure tractability. As examples, we show that all known classes of tractable constraints over finite domains can be characterized by such an algebraic closure property. Finally, we describe a simple computational procedure that can be used to determine the closure properties of a given set of constraints. This procedure involves solving a particular constraint satisfaction problem, which we call an “indicator problem.”