Tractable Combinations of Global Constraints
This work addresses a foundational problem in constraint programming for researchers and practitioners, but it appears incremental as it builds on prior work on individual constraints.
The paper tackles the complexity of constraint satisfaction problems with global constraints by identifying a new tractable class that combines structural restrictions with constraints that do not distinguish between large solution classes, resulting in a method for handling unbounded arity constraints.
We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used; indeed, they are one of the key reasons for the success of constraint programming in solving real-world problems. Previous work has focused on the development of efficient propagators for individual constraints. In this paper, we identify a new tractable class of constraint problems involving global constraints of unbounded arity. To do so, we combine structural restrictions with the observation that some important types of global constraint do not distinguish between large classes of equivalent solutions.