Lower Bounds for Kernelizations

Linear Kernelizations for Restricted 3-Hitting Set Problems

The 3-Hitting Set problem, also called the Vertex Cover problem on 3-uniform hypergraphs, cannot be solved in polynomial time unless P=NP. However, this problem is fixed-parameter tractable in the parameterized complexity, which means that it has kernelizations. In this paper, we address such kernelizations of the Vertex Cover problem on 3-uniform hypergraphs. Moreover, we show that this proble...

Kernelization of generic problems: upper and lower bounds

This thesis addresses the kernelization properties of generic problems, defined via syntactical restrictions or by a problem framework. Polynomial kernelization is a formalization of data reduction, aimed at combinatorially hard problems, which allows a rigorous study of this important and fundamental concept. The thesis is organized into two main parts. In the first part we prove that all prob...

Smaller Parameters for Vertex Cover Kernelization

We revisit the topic of polynomial kernels for Vertex Cover relative to structural parameters. Our starting point is a recent paper due to Fomin and Str{\o}mme [WG 2016] who gave a kernel with $\mathcal{O}(|X|^{12})$ vertices when $X$ is a vertex set such that each connected component of $G-X$ contains at most one cycle, i.e., $X$ is a modulator to a pseudoforest. We strongly generalize this re...

Two Edge Modification Problems without Polynomial Kernels

Given a graph G and an integer k, the Π Edge Completion/Editing/Deletion problem asks whether it is possible to add, edit, or delete at most k edges in G such that one obtains a graph that fulfills the property Π . Edge modification problems have received considerable interest from a parameterized point of view. When parameterized by k, many of these problems turned out to be fixed-parameter tr...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces