Fibonacci heaps and their uses in improved network optimization algorithms
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The State of the Art of Nurse Rostering
Journal of Scheduling
On global warming: Flow-based soft global constraints
Journal of Heuristics
Generalizations of the Global Cardinality Constraint for Hierarchical Resources
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Towards efficient consistency enforcement for global constraints in weighted constraint satisfaction
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Generalized arc consistency for global cardinality constraint
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Hybrid tractability of valued constraint problems
Artificial Intelligence
CP'11 Proceedings of the 17th international conference on Principles and practice of constraint programming
Tractable triangles and cross-free convexity in discrete optimisation
Journal of Artificial Intelligence Research
A characterisation of the complexity of forbidding subproblems in binary Max-CSP
CP'12 Proceedings of the 18th international conference on Principles and Practice of Constraint Programming
The tractability of CSP classes defined by forbidden patterns
Journal of Artificial Intelligence Research
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We introduce tractable classes of VCSP instances based on convex cost functions. Firstly, we show that the class of VCSP instances satisfying the hierarchically nested convexity property is tractable. This class generalises our recent results on VCSP instances satisfying the non-overlapping convexity property by dropping the assumption that the input functions are non-decreasing [3]. Not only do we generalise the tractable class from [3], but also our algorithm has better running time compared to the algorithm from [3]. We present several examples of applications including soft hierarchical global cardinality constraints, useful in rostering problems. We go on to show that, over Boolean domains, it is possible to determine in polynomial time whether there exists some subset of the constraints such that the VCSP satisfies the hierarchically nested convexity property after renaming the variables in these constraints.