Somnath Sikdar

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

The parameterized complexity of the induced matching problem

\mathcal{F}

Solving Dominating Set in Larger Classes of Graphs: FPT Algorithms and Polynomial Kernels

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

Simpler Parameterized Algorithm for OCT

\mathcal{F}

A New (2, n )-Visual Threshold Scheme for Color Images

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

FPT algorithms for Connected Feedback Vertex Set

|X|\leqslant k

Kernelization Using Structural Parameters on Sparse Graph Classes

and G−X is H-minor-free for every

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

H\in \mathcal{F}

Improved exact exponential algorithms for vertex bipartization and other problems

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

The parameterized complexity of the induced matching problem in planar graphs

\mathcal{F}