Comments on Mohr and Henderson's path consistency algorithm
Artificial Intelligence
An optimal k-consistency algorithm
Artificial Intelligence
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
Horn functions and submodular Boolean functions
Ordal'94 Selected papers from the conference on Orders, algorithms and applications
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)
Efficient and practical algorithms for sequential modular decomposition
Journal of Algorithms
A fully combinatorial algorithm for submodular function minimization
Journal of Combinatorial Theory Series B
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
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
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Constraint Processing
A note on the minimization of symmetric and general submodular functions
Discrete Applied Mathematics - Submodularity
Arc consistency for soft constraints
Artificial Intelligence
Solving weighted CSP by maintaining arc consistency
Artificial Intelligence
Linear-time modular decomposition of directed graphs
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
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
Bisubmodular Function Minimization
SIAM Journal on Discrete Mathematics
A dichotomy theorem for constraint satisfaction problems on a 3-element set
Journal of the ACM (JACM)
The Approximability of Three-valued MAX CSP
SIAM Journal on Computing
The complexity of soft constraint satisfaction
Artificial Intelligence
Minimum cost and list homomorphisms to semicomplete digraphs
Discrete Applied Mathematics
A faster strongly polynomial time algorithm for submodular function minimization
Mathematical Programming: Series A and B
A maximal tractable class of soft constraints
Journal of Artificial Intelligence Research
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
An algebraic characterisation of complexity for valued constraint
CP'06 Proceedings of the 12th international conference on Principles and Practice of Constraint Programming
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
A new hybrid tractable class of soft constraint problems
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Extensions of the minimum cost homomorphism problem
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
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
The complexity of conservative valued CSPs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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 complexity of conservative valued CSPs
Journal of the ACM (JACM)
Modularity-based decompositions for valued CSP
Annals of Mathematics and Artificial Intelligence
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
Hi-index | 5.23 |
The submodular function minimization problem (SFM) is a fundamental problem in combinatorial optimization and several fully combinatorial polynomial-time algorithms have recently been discovered to solve this problem. The most general versions of these algorithms are able to minimize any submodular function whose domain is a set of tuples over any totally-ordered finite set and whose range includes both finite and infinite values. In this paper we demonstrate that this general form of SFM is just one example of a much larger class of tractable discrete optimization problems defined by valued constraints. These tractable problems are characterized by the fact that their valued constraints have an algebraic property which we call a tournament pair multimorphism. This larger tractable class also includes the problem of satisfying a set of Horn clauses (Horn-SAT), as well as various extensions of this problem to larger finite domains.