Ignasi Sau

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

Hardness and approximation of traffic grooming

\mathcal{F}

Degree-Constrained Subgraph Problems: Hardness and Approximation Results

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

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

\mathcal{F}

A New Intersection Model and Improved Algorithms for Tolerance Graphs

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

The Recognition of Tolerance and Bounded Tolerance Graphs

|X|\leqslant k

Subexponential parameterized algorithms for degree-constrained subgraph problems on planar graphs

and G−X is H-minor-free for every

Dynamic programming for graphs on surfaces

H\in \mathcal{F}

Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

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

Explicit Linear Kernels via Dynamic Programming

\mathcal{F}