Recognizing frozen variables in constraint satisfaction problems
Theoretical Computer Science
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
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
Determining the consistency of partial tree descriptions
Artificial Intelligence
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
Domain permutation reduction for constraint satisfaction problems
Artificial Intelligence
Majority constraints have bounded pathwidth duality
European Journal of Combinatorics
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
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
Non-dichotomies in Constraint Satisfaction Complexity
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Quantified Constraint Satisfaction and the Polynomially Generated Powers Property
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part II
Classes of Submodular Constraints Expressible by Graph Cuts
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
The expressive power of valued constraints: Hierarchies and collapses
Theoretical Computer Science
There are no pure relational width 2 constraint satisfaction problems
Information Processing Letters
Recent Results on the Algebraic Approach to the CSP
Complexity of Constraints
Dualities for Constraint Satisfaction Problems
Complexity of Constraints
A Logical Approach to Constraint Satisfaction
Complexity of Constraints
Constraint Satisfaction Problems with Infinite Templates
Complexity of Constraints
Introduction to the Maximum Solution Problem
Complexity of Constraints
Affine systems of equations and counting infinitary logic
Theoretical Computer Science
Maximal infinite-valued constraint languages
Theoretical Computer Science
A note on some collapse results of valued constraints
Information Processing Letters
Tricolorable torus knots are NP-complete
Proceedings of the 47th Annual Southeast Regional Conference
Hybrid tractable CSPs which generalize tree structure
Proceedings of the 2008 conference on ECAI 2008: 18th European Conference on Artificial Intelligence
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
Information and Computation
Hard constraint satisfaction problems have hard gaps at location 1
Theoretical Computer Science
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
Trichotomy Results on the Complexity of Reasoning with Disjunctive Logic Programs
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
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 combinatorial constraint satisfaction problem dichotomy classification conjecture
European Journal of Combinatorics
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
A fast algorithm and datalog inexpressibility for temporal reasoning
ACM Transactions on Computational Logic (TOCL)
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
Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination
Artificial Intelligence
Computational complexity of generalized domination: a complete dichotomy for chordal graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
Constraint representations and structural tractability
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
The complexity of valued constraint models
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Proceedings of the forty-second ACM symposium on Theory of computing
CSP duality and trees of bounded pathwidth
Theoretical Computer Science
Minimum cost homomorphisms to oriented cycles with some loops
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Distance constraint satisfaction problems
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Testing expressibility is hard
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A new hybrid tractable class of soft constraint problems
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
On the phase transitions of random k-constraint satisfaction problems
Artificial Intelligence
Maltsev digraphs have a majority polymorphism
European Journal of Combinatorics
Congruence Distributivity Implies Bounded Width
SIAM Journal on Computing
Tractability and Learnability Arising from Algebras with Few Subpowers
SIAM Journal on Computing
A New Proof of the $H$-Coloring Dichotomy
SIAM Journal on Discrete Mathematics
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
Hybrid tractability of valued constraint problems
Artificial Intelligence
Note: The Ck-extended graft construction
Discrete Applied Mathematics
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
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
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
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 computational complexity of disconnected cut and 2K2-partition
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Quantified Equality Constraints
SIAM Journal on Computing
Linear programming, width-1 CSPs, and robust satisfaction
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Approximability of integer programming with generalised constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Locally injective graph homomorphism: lists guarantee dichotomy
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Generalised dualities and finite maximal antichains
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
The complexity of equality constraint languages
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Datalog and constraint satisfaction with infinite templates
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Towards a trichotomy for quantified H-coloring
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Journal of Computer and System Sciences
Collapsibility in infinite-domain quantified constraint satisfaction
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
Universal structures and the logic of forbidden patterns
CSL'06 Proceedings of the 20th international conference on Computer Science Logic
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
Trichotomy and dichotomy results on the complexity of reasoning with disjunctive logic programs
Theory and Practice of Logic Programming
Robust satisfiability of constraint satisfaction problems
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
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
SIAM Journal on Discrete Mathematics
Meditations on quantified constraint satisfaction
Logic and Program Semantics
Near Unanimity Constraints Have Bounded Pathwidth Duality
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Tractable triangles and cross-free convexity in discrete optimisation
Journal of Artificial Intelligence Research
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
Combinatorial proof that subprojective constraint satisfaction problems are NP-complete
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Qualitative temporal and spatial reasoning revisited
CSL'07/EACSL'07 Proceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic
Maximal infinite-valued constraint languages
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Affine systems of equations and counting infinitary logic
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Datalog and constraint satisfaction with infinite templates
Journal of Computer and System Sciences
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
Weak near-unanimity functions and digraph homomorphism problems
Theoretical Computer Science
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
The complexity of finite-valued CSPs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Qualitative constraint satisfaction problems: An extended framework with landmarks
Artificial Intelligence
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)
Constraint satisfaction tractability from semi-lattice operations on infinite sets
ACM Transactions on Computational Logic (TOCL)
Diagnosing correctness of semantic workflow models
Data & Knowledge Engineering
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)
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Many natural combinatorial problems can be expressed as constraint satisfaction problems. This class of problems is known to be NP-complete in general, but certain restrictions on the form of the constraints can ensure tractability. Here we show that any set of relations used to specify the allowed forms of constraints can be associated with a finite universal algebra and we explore how the computational complexity of the corresponding constraint satisfaction problem is connected to the properties of this algebra. Hence, we completely translate the problem of classifying the complexity of restricted constraint satisfaction problems into the language of universal algebra.We introduce a notion of "tractable algebra," and investigate how the tractability of an algebra relates to the tractability of the smaller algebras which may be derived from it, including its subalgebras and homomorphic images. This allows us to reduce significantly the types of algebras which need to be classified. Using our results we also show that if the decision problem associated with a given collection of constraint types can be solved efficiently, then so can the corresponding search problem. We then classify all finite strictly simple surjective algebras with respect to tractability, obtaining a dichotomy theorem which generalizes Schaefer's dichotomy for the generalized satisfiability problem. Finally, we suggest a possible general algebraic criterion for distinguishing the tractable and intractable cases of the constraint satisfaction problem.