The approximability of MAX CSP with fixed-value constraints
Journal of the ACM (JACM)
Note: The expressive power of binary submodular functions
Discrete Applied Mathematics
Submodularity on a tree: unifying L-convex and bisubmodular functions
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Min CSP on four elements: moving beyond submodularity
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Survey: Colouring, constraint satisfaction, and complexity
Computer Science Review
On the complexity of submodular function minimisation on diamonds
Discrete Optimization
Towards minimizing k-submodular functions
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
The complexity of conservative valued CSPs
Journal of the ACM (JACM)
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Recently, a strong link has been discovered between supermodularity on lattices and tractability of optimization problems known as maximum constraint satisfaction problems. This paper strengthens this link. We study the problem of maximizing a supermodular function which is defined on a product of $n$ copies of a fixed finite lattice and given by an oracle. We exhibit a large class of finite lattices for which this problem can be solved in oracle-polynomial time in $n$. We also obtain new large classes of tractable maximum constraint satisfaction problems.