Related papers: Preprocessing Complexity for Some Graph Problems P…
In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of…
Graph kernels have attracted a lot of attention during the last decade, and have evolved into a rapidly developing branch of learning on structured data. During the past 20 years, the considerable research activity that occurred in the…
Structural graph parameters, such as treewidth, pathwidth, and clique-width, are a central topic of study in parameterized complexity. A main aim of research in this area is to understand the "price of generality" of these widths: as we…
Kernelization is a formalization of efficient preprocessing for NP-hard problems using the framework of parameterized complexity. Among open problems in kernelization it has been asked many times whether there are deterministic polynomial…
Vertex deletion and edge deletion problems play a central role in Parameterized Complexity. Examples include classical problems like Feedback Vertex Set, Odd Cycle Transversal, and Chordal Deletion. Interestingly, the study of edge…
Many graph problems were first shown to be fixed-parameter tractable using the results of Robertson and Seymour on graph minors. We show that the combination of finite, computable, obstruction sets and efficient order tests is not just one…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
We study kernelization of classic hard graph problems when the input graphs fulfill triadic closure properties. More precisely, we consider the recently introduced parameters closure number $c$ and the weak closure number $\gamma$ [Fox et…
The graph crossing number problem, cr(G)<=k, asks for a drawing of a graph G in the plane with at most k edge crossings. Although this problem is in general notoriously difficult, it is fixed- parameter tractable for the parameter k…
The framework of Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam (STOC 2008) allows us to exclude the existence of polynomial kernels for a range of problems under reasonable complexity-theoretical assumptions. However, there are…
After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to…
The Odd Cycle Transversal problem (OCT) asks whether a given graph can be made bipartite (i.e., 2-colorable) by deleting at most l vertices. We study structural parameterizations of OCT with respect to their polynomial kernelizability,…
Temporal graphs provide a useful model for many real-world networks. Unfortunately the majority of algorithmic problems we might consider on such graphs are intractable. There has been recent progress in defining structural parameters which…
The Vertex Cover problem plays an essential role in the study of polynomial kernelization in parameterized complexity, i.e., the study of provable and efficient preprocessing for NP-hard problems. Motivated by the great variety of positive…
A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring $c$ of a mixed graph $G$ assigns a positive integer to each vertex such that $c(u)\neq c(v)$ for every…
Graph parameters such as the clique number, the chromatic number, and the independence number are central in many areas, ranging from computer networks to linguistics to computational neuroscience to social networks. In particular, the…
We extend the notion of lossy kernelization, introduced by Lokshtanov et al. [STOC 2017], to approximate Turing kernelization. An $\alpha$-approximate Turing kernel for a parameterized optimization problem is a polynomial-time algorithm…
Many algorithms for ranked data become computationally intractable as the number of objects grows due to the complex geometric structure induced by rankings. An additional challenge is posed by partial rankings, i.e. rankings in which the…
We study efficient preprocessing for the undirected Feedback Vertex Set problem, a fundamental problem in graph theory which asks for a minimum-sized vertex set whose removal yields an acyclic graph. More precisely, we aim to determine for…
Given a graph $G$ and a positive integer $k$, the 2-Load coloring problem is to check whether there is a $2$-coloring $f:V(G) \rightarrow \{r,b\}$ of $G$ such that for every $i \in \{r,b\}$, there are at least $k$ edges with both end…