Integer and combinatorial optimization
Integer and combinatorial optimization
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
On the supermodular knapsack problem
Mathematical Programming: Series A and B
Recognition problems for special classes of polynomials in 0-1 variables
Mathematical Programming: Series A and B
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
Discrete Applied Mathematics
Constraint Processing
What Energy Functions Can Be Minimizedvia Graph Cuts?
IEEE Transactions on Pattern Analysis and Machine Intelligence
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Fields of Experts: A Framework for Learning Image Priors
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Energy Minimization via Graph Cuts: Settling What is Possible
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
The Approximability of Three-valued MAX CSP
SIAM Journal on Computing
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
Submodular function minimization
Mathematical Programming: Series A and B
Maximizing Non-Monotone Submodular Functions
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
A faster strongly polynomial time algorithm for submodular function minimization
Mathematical Programming: Series A and B
A simple combinatorial algorithm for submodular function minimization
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Robust Higher Order Potentials for Enforcing Label Consistency
International Journal of Computer Vision
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Constraints, consistency and closure
Artificial Intelligence
The complexity of soft constraint satisfaction
Artificial Intelligence
Supermodular functions and the complexity of MAX CSP
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Communication: Level of repair analysis and minimum cost homomorphisms of graphs
Discrete Applied Mathematics
An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
Efficient belief propagation with learned higher-order markov random fields
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Texture synthesis via a noncausal nonparametric multiscale Markov random field
IEEE Transactions on Image Processing
Minimizing a sum of submodular functions
Discrete Applied Mathematics
Discrete Applied Mathematics
Generic cuts: an efficient algorithm for optimal inference in higher order MRF-MAP
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part V
The expressibility of functions on the boolean domain, with applications to counting CSPs
Journal of the ACM (JACM)
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Submodular constraints play an important role both in theory and practice of valued constraint satisfaction problems (VCSPs). It has previously been shown, using results from the theory of combinatorial optimisation, that instances of VCSPs with submodular constraints can be minimised in polynomial time. However, the general algorithm is of order O(n 6) and hence rather impractical. In this paper, by using results from the theory of pseudo-Boolean optimisation, we identify several broad classes of submodular constraints over a Boolean domain which are expressible using binary submodular constraints, and hence can be minimised in cubic time. Furthermore, we describe how our results translate to certain optimisation problems arising in computer vision.