Network-based heuristics for constraint-satisfaction problems
Artificial Intelligence
A filtering algorithm for constraints of difference in CSPs
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
On the algebraic structure of combinatorial problems
Theoretical Computer Science
Scheduling independent tasks to reduce mean finishing time
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Specific Filtering Algorithms for Over-Constrained Problems
CP '01 Proceedings of the 7th International Conference on Principles and Practice of Constraint Programming
Constraint Processing
Classifying the Complexity of Constraints Using Finite Algebras
SIAM Journal on Computing
Combinatorica
On global warming: Flow-based soft global constraints
Journal of Heuristics
The complexity of homomorphism and constraint satisfaction problems seen from the other side
Journal of the ACM (JACM)
A Framework for Hybrid Tractability Results in Boolean Weighted Constraint Satisfaction Problems
CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
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
Towards efficient consistency enforcement for global constraints in weighted constraint satisfaction
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Generalizing constraint satisfaction on trees: Hybrid tractability and variable elimination
Artificial Intelligence
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The constraint satisfaction problem (CSP) is a central generic problem in artificial intelligence. Considerable effort has been made in identifying properties which ensure tractability in such problems. In this paper we study hybrid tractability of soft constraint problems; that is, properties which guarantee tractability of the given soft constraint problem, but properties which do not depend only on the underlying structure of the instance (such as being tree-structured) or only on the types of soft constraints in the instance (such as submodularity). We firstly present two hybrid classes of soft constraint problems defined by forbidden subgraphs in the structure of the instance. These classes allow certain combinations of binary crisp constraints together with arbitrary unary soft constraints. We then introduce the joint-winner property, which allows us to define a novel hybrid tractable class of soft constraint problems with soft binary and unary constraints. This class generalises the SOFTAllDIFF constraint with arbitrary unary soft constraints. We show that the joint-winner property is easily recognisable in polynomial time and present a polynomial-time algorithm based on maximum-flows for the class of soft constraint problems satisfying the joint-winner property. Moreover, we show that if cost functions can only take on two distinct values then this class is maximal.