Hierarchically Nested Convex VCSP

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. 1 Preliminaries VCSPs As usual, we denote by N the set of positive int...

• Type: Journal
• Year: 2011
• Where: CP
• Authors: Martin C. Cooper, Stanislav Zivny
• Keywords: Artificial Intelligence, Cardinality Constraints, Constraint Satisfaction Problem, CP 2011, Polynomial Time