Propagation via Kernelization: The Vertex Cover Constraint

The technique of kernelization consists in extracting, from an instance of a problem, an essentially equivalent instance whose size is bounded in a parameter \(k\). Besides being the basis for efficient parameterized algorithms, this method also provides a wealth of information to reason about in the context of constraint programming. We study the use of kernelization for designing propagators through the example of the Vertex Cover constraint. Since the classic kernelization rules often correspond to dominance rather than consistency, we introduce the notion of “loss-less” kernel. While our preliminary experimental results show the potential of the approach, they also show some of its limits. In particular, this method is more effective for vertex covers of large and sparse graphs, as they tend to have, relatively, smaller kernels.