On submodular function minimization
Combinatorica
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
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
A combinatorial algorithm minimizing submodular functions in strongly polynomial time
Journal of Combinatorial Theory Series B
Realization of set functions as cut functions of graphs and hypergraphs
Discrete Mathematics
A combinatorial strongly polynomial algorithm for minimizing submodular functions
Journal of the ACM (JACM)
A fully combinatorial algorithm for submodular function minimization
Journal of Combinatorial Theory Series B
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Discrete Applied Mathematics
Reduction operations in fuzzy or valued constraint satisfaction
Fuzzy Sets and Systems - Optimisation and decision
Tractable conservative Constraint Satisfaction Problems
LICS '03 Proceedings of the 18th Annual IEEE Symposium on Logic in Computer Science
Constraint Processing
Arc consistency for soft constraints
Artificial Intelligence
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
The Approximability of Three-valued MAX CSP
SIAM Journal on Computing
The complexity of soft constraint satisfaction
Artificial Intelligence
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
A Linear Programming Approach to Max-Sum Problem: A Review
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Faster Strongly Polynomial Time Algorithm for Submodular Function Minimization
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Refining the basic constraint propagation algorithm
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Exact solution of permuted submodular minsum problems
EMMCVPR'07 Proceedings of the 6th international conference on Energy minimization methods in computer vision and pattern recognition
An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Generalized arc consistency for positive table constraints
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
The partial constraint satisfaction problem: Facets and lifting theorems
Operations Research Letters
Classes of Submodular Constraints Expressible by Graph Cuts
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
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
Soft arc consistency revisited
Artificial Intelligence
Preferences in AI: An overview
Artificial Intelligence
Higher order Markov networks for model estimation
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part I
Minimizing a sum of submodular functions
Discrete Applied Mathematics
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Submodular function minimization is a polynomially solvable combinatorial problem. Unfortunately the best known general-purpose algorithms have high-order polynomial time complexity. In many applications the objective function is locally defined in that it is the sum of cost functions (also known as soft or valued constraints) whose arities are bounded by a constant. We prove that every valued constraint satisfaction problem with submodular cost functions has an equivalent instance on the same constraint scopes in which the actual minimum value of the objective function is rendered explicit. Such an equivalent instance is the result of establishing optimal soft arc consistency and can hence be found by solving a linear program. From a practical point of view, this provides us with an alternative algorithm for minimizing locally defined submodular functions. From a theoretical point of view, this brings to light a previously unknown connection between submodularity and soft arc consistency.