Felix Reidl

Linear kernels and single-exponential algorithms via protrusion decompositions

We present a linear-time algorithm to compute a decomposition scheme for graphs G that have a set X⊆V(G), called a treewidth-modulator, such that the treewidth of G−X is bounded by a constant. Our decomposition, called a protrusion decomposition, is the cornerstone in obtaining the following two main results. Our first result is that any parameterized graph problem (with parameter k) that has finite integer index and such that positive instances have a treewidth-modulator of size O(k) admits a linear kernel on the class of H-topological-minor-free graphs, for any fixed graph H. This result partially extends previous meta-theorems on the existence of linear kernels on graphs of bounded genus and H-minor-free graphs. Let

Kernelization Using Structural Parameters on Sparse Graph Classes

\mathcal{F}

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

be a fixed finite family of graphs containing at least one planar graph. Given an n-vertex graph G and a non-negative integer k, Planar

Practical algorithms for MSO model-checking on tree-decomposable graphs

\mathcal{F}

Kernelization and Sparseness: the Case of Dominating Set

- Deletion asks whether G has a set X⊆V(G) such that

A Faster Parameterized Algorithm for Treedepth

|X|\leqslant k

Kernelization using structural parameters on sparse graph classes

and G−X is H-minor-free for every

Characterising bounded expansion by neighbourhood complexity

H\in \mathcal{F}

Hyperbolicity, Degeneracy, and Expansion of Random Intersection Graphs

. As our second application, we present the first single-exponential algorithm to solve Planar

Air-Indexing on error prone communication channels

\mathcal{F}