On approximate preprocessing for domination and hitting subgraphs with connected deletion sets

摘要

In this paper, we study the Connected H-hitting Set and Dominating Set problems from the perspective of approximate kernelization, a framework recently introduced by Lokshtanov et al. [STOC 2017]. For the Connected H-hitting set problem, we obtain an α-approximate kernel for every α>1 and complement it with a lower bound for the natural weighted version. We then perform a refined analysis of the tradeoff between the approximation factor and kernel size for the Dominating Set problem on d-degenerate graphs, and provide an interpolation of approximate kernels between the known 3d-approximate kernel of constant size and 1-approximate kernel of size kO(d2).