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
The complexity of constraint satisfaction revisited
Artificial intelligence in perspective
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
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)
Level of repair analysis and minimum cost homomorphisms of graphs
Discrete Applied Mathematics
Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
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
Constraints, consistency and closure
Artificial Intelligence
A Semantic Foundation for Trust Management Languages with Weights: An Application to the RT Family
ATC '08 Proceedings of the 5th international conference on Autonomic and Trusted Computing
Classes of Submodular Constraints Expressible by Graph Cuts
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
Introduction to the Maximum Solution Problem
Complexity of Constraints
Soft arc consistency revisited
Artificial Intelligence
The expressive power of valued constraints: hierarchies and collapses
CP'07 Proceedings of the 13th 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
A new hybrid tractable class of soft constraint problems
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
A weighted CSP approach to cost-optimal planning
AI Communications
Preferences in AI: An overview
Artificial Intelligence
Hybrid tractability of valued constraint problems
Artificial Intelligence
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
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Min CSP on four elements: moving beyond submodularity
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
An algebraic characterisation of complexity for valued constraint
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
On the complexity of submodular function minimisation on diamonds
Discrete Optimization
Computers & Mathematics with Applications
A Nonmonotonic Soft Concurrent Constraint Language to Model the Negotiation Process
Fundamenta Informaticae
Towards minimizing k-submodular functions
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Tractable triangles and cross-free convexity in discrete optimisation
Journal of Artificial Intelligence Research
The maximum solution problem on graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
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
The power of linear programming for finite-valued CSPs: a constructive characterization
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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
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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.