Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
An optimal k-consistency algorithm
Artificial Intelligence
From local to global consistency
Artificial Intelligence
A generic arc-consistency algorithm and its specializations
Artificial Intelligence
Experimental evaluation of preprocessing algorithms for constraint satisfaction problems
Artificial Intelligence
Constraint satisfaction in Prolog: complexity and theory-based heuristics
Information Sciences—Intelligent Systems: An International Journal
Structure-driven algorithms for truth maintenance
Artificial Intelligence
Local and global relational consistency
Theoretical Computer Science - Special issue: principles and practice of constraint programming
Closure properties of constraints
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Constraints, consistency and closure
Artificial Intelligence
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
A Sufficient Condition for Backtrack-Free Search
Journal of the ACM (JACM)
Constraint satisfaction and database theory: a tutorial
PODS '00 Proceedings of the nineteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Conjunctive-query containment and constraint satisfaction
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
A comparison of structural CSP decomposition methods
Artificial Intelligence
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
The complexity of maximal constraint languages
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Universal Algebra and Applications in Theoretical Computer Science
Universal Algebra and Applications in Theoretical Computer Science
Constraints and universal algebra
Annals of Mathematics and Artificial Intelligence
Temporal Constraints: A Survey
Constraints
A Game-Theoretic Approach to Constraint Satisfaction
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Constraint satisfaction, databases, and logic
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
The complexity of soft constraint satisfaction
Artificial Intelligence
A rendezvous of logic, complexity, and algebra
ACM SIGACT News
Maximum H-colourable subdigraphs and constraint optimization with arbitrary weights
Journal of Computer and System Sciences
Computational complexity of auditing finite attributes in statistical databases
Journal of Computer and System Sciences
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
Computational Complexity of Constraint Satisfaction
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Quantified Constraint Satisfaction and the Polynomially Generated Powers Property
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
There are no pure relational width 2 constraint satisfaction problems
Information Processing Letters
Relatively quantified constraint satisfaction
Constraints
Recent Results on the Algebraic Approach to the CSP
Complexity of Constraints
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
Partial Polymorphisms and Constraint Satisfaction Problems
Complexity of Constraints
Introduction to the Maximum Solution Problem
Complexity of Constraints
On the Computational Complexity of Monotone Constraint Satisfaction Problems
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
Holant problems and counting CSP
Proceedings of the forty-first annual ACM symposium on Theory of computing
A new line of attack on the dichotomy conjecture
Proceedings of the forty-first annual ACM symposium on Theory of computing
Hybrid tractable CSPs which generalize tree structure
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
A rendezvous of logic, complexity, and algebra
ACM Computing Surveys (CSUR)
The complexity of constraint satisfaction games and QCSP
Information and Computation
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
The complexity of soft constraint satisfaction
Artificial Intelligence
The Helly property and satisfiability of Boolean formulas defined on set families
European Journal of Combinatorics
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
Enumerating all solutions for constraint satisfaction problems
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination
Artificial Intelligence
Proceedings of the forty-second ACM symposium on Theory of computing
Constraint satisfaction problems and global cardinality constraints
Communications of the ACM
CSP duality and trees of bounded pathwidth
Theoretical Computer Science
On the Boolean connectivity problem for Horn relations
Discrete Applied Mathematics
The lattice structure of sets of surjective hyper-operations
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
The complexity of positive first-order logic without equality II: the four-element case
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Congruence Distributivity Implies Bounded Width
SIAM Journal on Computing
Tractability and Learnability Arising from Algebras with Few Subpowers
SIAM Journal on Computing
A Complexity Dichotomy for Partition Functions with Mixed Signs
SIAM Journal on Computing
SIAM Journal on Discrete Mathematics
Complexity of conservative constraint satisfaction problems
ACM Transactions on Computational Logic (TOCL)
On the CSP dichotomy conjecture
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
The complexity of symmetric Boolean parity Holant problems
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Generic expression hardness results for primitive positive formula comparison
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Low-level dichotomy for quantified constraint satisfaction problems
Information Processing Letters
Spin systems on graphs with complex edge functions and specified degree regularities
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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
Submodularity on a tree: unifying L-convex and bisubmodular functions
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
QCSP on partially reflexive forests
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
The Complexity of Positive First-Order Logic without Equality
ACM Transactions on Computational Logic (TOCL)
Guest column: complexity dichotomies of counting problems
ACM SIGACT News
Computational Complexity of Holant Problems
SIAM Journal on Computing
Gadgets and anti-gadgets leading to a complexity dichotomy
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
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 conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Journal of Computer and System Sciences
The dichotomy of list homomorphisms for digraphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
The structure of tractable constraint satisfaction problems
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Complexity of counting CSP with complex weights
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
The complexity of surjective homomorphism problems-a survey
Discrete Applied Mathematics
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Minimization for generalized Boolean formulas
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
Meditations on quantified constraint satisfaction
Logic and Program Semantics
Spin systems on k-regular graphs with complex edge functions
Theoretical Computer Science
Ruling out polynomial-time approximation schemes for hard constraint satisfaction problems
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
The complexity of approximating bounded-degree Boolean #CSP
Information and Computation
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Containment, equivalence and coreness from CSP to QCSP and beyond
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
Generic expression hardness results for primitive positive formula comparison
Information and Computation
The tractability of CSP classes defined by forbidden patterns
Journal of Artificial Intelligence Research
Journal of Artificial Intelligence Research
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
Lee-Yang theorems and the complexity of computing averages
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
The complexity of three-element min-sol and conservative min-cost-hom
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
The complexity of the counting constraint satisfaction problem
Journal of the ACM (JACM)
The complexity of complex weighted Boolean #CSP
Journal of Computer and System Sciences
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
Robust Satisfiability for CSPs: Hardness and Algorithmic Results
ACM Transactions on Computation Theory (TOCT)
Constraint Satisfaction Problems Solvable by Local Consistency Methods
Journal of the ACM (JACM)
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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The Constraint Satisfaction Problem (CSP) provides a common framework for many combinatorial problems. The general CSP is known to be NP-complete; however, certain restrictions on a possible form of constraints may affect the complexity and lead to tractable problem classes. There is, therefore, a fundamental research direction, aiming to separate those subclasses of the CSP that are tractable and those which remain NP-complete.Schaefer gave an exhaustive solution of this problem for the CSP on a 2-element domain. In this article, we generalise this result to a classification of the complexity of the CSP on a 3-element domain. The main result states that every subproblem of the CSP is either tractable or NP-complete, and the criterion separating them is that conjectured in Bulatov et al. [2005] and Bulatov and Jeavons [2001b]. We also characterize those subproblems for which standard constraint propagation techniques provide a decision procedure. Finally, we exhibit a polynomial time algorithm which, for a given set of allowed constraints, outputs if this set gives rise to a tractable problem class. To obtain the main result and the algorithm, we extensively use the algebraic technique for the CSP developed in Jeavons [1998b], Bulatov et al.[2005], and Bulatov and Jeavons [2001b].