Integer and combinatorial optimization
Integer and combinatorial optimization
Partial constraint satisfaction
Artificial Intelligence - Special volume on constraint-based reasoning
A generic arc-consistency algorithm and its specializations
Artificial Intelligence
Fast parallel constraint satisfaction
Artificial Intelligence
Characterising tractable constraints
Artificial Intelligence
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
A dichotomy theorem for maximum generalized satisfiability problems
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Tractable constraints on ordered domains
Artificial Intelligence
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
Maintaining reversible DAC for Max-CSP
Artificial Intelligence
Improved algorithms for submodular function minimization and submodular flow
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
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
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
Constraints and universal algebra
Annals of Mathematics and Artificial Intelligence
Discrete Applied Mathematics
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Generalized Majority-Minority Operations are Tractable
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
Constraint solving over semirings
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Temporal constraint reasoning with preferences
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Communication: Level of repair analysis and minimum cost homomorphisms of graphs
Discrete Applied Mathematics
Communication: Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
Maximum H-colourable subdigraphs and constraint optimization with arbitrary weights
Journal of Computer and System Sciences
The expressive power of valued constraints: Hierarchies and collapses
Theoretical Computer Science
A Nonmonotonic Soft Concurrent Constraint Language for SLA Negotiation
Electronic Notes in Theoretical Computer Science (ENTCS)
A note on some collapse results of valued constraints
Information Processing Letters
Soft Constraints Processing over Divisible Residuated Lattices
ECSQARU '09 Proceedings of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
Virtual Arc consistency for weighted CSP
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
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Over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types. One very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations, known as polymorphisms.In this paper we extend the analysis of complexity to the more general framework of combinatorial optimisation problems expressed using various forms of soft constraints. We launch a systematic investigation of the complexity of these problems by extending the notion of a polymorphism to a more general algebraic operation, which we call a multimorphism. We show that many tractable sets of soft constraints, both established and novel, can be characterised by the presence of particular multimorphisms. We also show that a simple set of NP-hard constraints has very restricted multimorphisms. Finally, we use the notion of multimorphism to give a complete classification of complexity for the Boolean case which extends several earlier classification results for particular special cases.