Related papers: Kernelizing Problems on Planar Graphs in Sublinear…
Let $n$ be the size of a parameterized problem and $k$ the parameter. We present kernels for Feedback Vertex Set, Path Contraction and Cluster Editing/Deletion whose sizes are all polynomial in $k$ and that are computable in polynomial time…
We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an…
Kernelization studies polynomial-time preprocessing algorithms. Over the last 20 years, the most celebrated positive results of the field have been linear kernels for classical NP-hard graph problems on sparse graph classes. In this paper,…
Subexponential parameterized algorithms are known for a wide range of natural problems on planar graphs, but the techniques are usually highly problem specific. The goal of this paper is to introduce a framework for obtaining…
A kernelization for a parameterized decision problem $\mathcal{Q}$ is a polynomial-time preprocessing algorithm that reduces any parameterized instance $(x,k)$ into an instance $(x',k')$ whose size is bounded by a function of $k$ alone and…
We prove the following theorem. Given a planar graph $G$ and an integer $k$, it is possible in polynomial time to randomly sample a subset $A$ of vertices of $G$ with the following properties: (i) $A$ induces a subgraph of $G$ of treewidth…
Kernelization algorithms are polynomial-time reductions from a problem to itself that guarantee their output to have a size not exceeding some bound. For example, d-Set Matching for integers d>2 is the problem of finding a matching of size…
We investigate whether kernelization results can be obtained if we restrict kernelization algorithms to run in logarithmic space. This restriction for kernelization is motivated by the question of what results are attainable for…
There are existing standard solvers for tackling discrete optimization problems. However, in practice, it is uncommon to apply them directly to the large input space typical of this class of problems. Rather, the input is preprocessed to…
In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the…
The field of kernelization studies polynomial-time preprocessing routines for hard problems in the framework of parameterized complexity. Although a framework for proving kernelization lower bounds has been discovered in 2008 and…
Kernelization is an important tool in parameterized algorithmics. Given an input instance accompanied by a parameter, the goal is to compute in polynomial time an equivalent instance of the same problem such that the size of the reduced…
Dealing with the NP-complete Dominating Set problem on undirected graphs, we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side. In particular, we prove that Dominating Set restricted to…
The notion of a (polynomial) kernelization from parameterized complexity is a well-studied model for efficient preprocessing for hard computational problems. By now, it is quite well understood which parameterized problems do or…
The notion of Turing kernelization investigates whether a polynomial-time algorithm can solve an NP-hard problem, when it is aided by an oracle that can be queried for the answers to bounded-size subproblems. One of the main open problems…
We describe a linear-time algorithm that finds a planar drawing of every graph of a simple line or pseudoline arrangement within a grid of area O(n^{7/6}). No known input causes our algorithm to use area \Omega(n^{1+\epsilon}) for any…
The theoretical notions of graph classes with bounded expansion and that are nowhere dense are meant to capture structural sparsity of real world networks that can be used to design efficient algorithms. In the area of sparse graphs, the…
We study a general family of facility location problems defined on planar graphs and on the 2-dimensional plane. In these problems, a subset of $k$ objects has to be selected, satisfying certain packing (disjointness) and covering…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
We develop two different methods to achieve subexponential time parameterized algorithms for problems on sparse directed graphs. We exemplify our approaches with two well studied problems. For the first problem, {\sc $k$-Leaf…