Alexander Langer

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

An exact algorithm for the Maximum Leaf Spanning Tree problem

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Courcelle’s theorem—A game-theoretic approach

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

A Fine-grained Analysis of a Simple Independent Set Algorithm

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On Digraph Width Measures in Parameterized Algorithmics

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

A New Algorithm for Finding Trees with Many Leaves

|X|\leqslant k

Improved Upper Bounds for Partial Vertex Cover

and G−X is H-minor-free for every

Digraph width measures in parameterized algorithmics

H\in \mathcal{F}

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

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

Breaking the 2n-barrier for Irredundance: Two lines of attack

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