A new approach to the maximum-flow problem
Journal of the ACM (JACM)
Journal of the ACM (JACM)
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
A note on the minimization of symmetric and general submodular functions
Discrete Applied Mathematics - Submodularity
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
Handbook of Constraint Programming (Foundations of Artificial Intelligence)
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
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
The complexity of soft constraint satisfaction
Artificial Intelligence
Hi-index | 0.00 |
The VALUED CONSTRAINT SATISFACTION PROBLEM (VCSP) is a general framework encompassing many optimisation problems. We discuss precisely what it means for a problem to be modelled in the VCSP framework. Using our analysis, we show that some optimisation problems, such as (s, t)-MIN-CUT and SUBMODULAR FUNCTION MINIMISATION, can be modelled using a restricted set of valued constraints which are tractable to solve regardless of how they are combined. Hence, these problems can be viewed as special cases of more general problems which include all possible instances using the same forms of valued constraint. However, other, apparently similar, problems such as MIN-CUT and SYMMETRIC SUBMODULAR FUNCTION MINIMISATION, which also have polynomial-time algorithms, can only be naturally modelled in the VCSP framework by using valued constraints which can represent NP-complete problems. This suggests that the reason for tractability in these problems is more subtle; it relies not only on the form of the valued constraints, but also on the precise structure of the problem. Furthermore, our results suggest that allowing constant constraints can significantly alter the complexity of problems in the VCSP framework, in contrast to the CSP framework.