The Buss Reduction for the k-Weighted Vertex Cover Problem

The k-vertex cover (k-VC) problem is to find a VC of cardinality no more than k on a given undirected graph, and the k-weighted VC (k-WVC) problem is to find a VC of a weight no more than k on a given vertex-weighted undirected graph. In this paper, we generalize the Buss reduction, an important kernelization technique for the k-VC problem, to the kWVC problem. We study its properties for the k-VC problem and the k-WVC problem on surrogates of large real-world graphs that are generated using the Erdős-Rényi model and the Barabási-Albert model. We also argue that our study of the Buss reduction bears important implications on the kernelization of combinatorial problems that have been shown to be reducible to WVC problems.