相关论文: What is known about Vertex Cover Kernelization?
The notion of treewidth plays an important role in theoretical and practical studies of graph problems. It has been recognized that, especially in practical environments, when computing the treewidth of a graph it is invaluable to first…
In the Vertex Planarization problem one asks to delete the minimum possible number of vertices from an input graph to obtain a planar graph. The parameterized complexity of this problem, parameterized by the solution size (the number of…
For a fixed graph $H$, the $H$-SUBGRAPH HITTING problem consists in deleting the minimum number of vertices from an input graph to obtain a graph without any occurrence of $H$ as a subgraph. This problem can be seen as a generalization of…
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,…
For a given graph $G$, a depth-first search (DFS) tree $T$ of $G$ is an $r$-rooted spanning tree such that every edge of $G$ is either an edge of $T$ or is between a \textit{descendant} and an \textit{ancestor} in $T$. A graph $G$ together…
In the Maximum Minimal Vertex Cover (MMVC) problem, we are given a graph $G$ and a positive integer $k$, and the objective is to decide whether $G$ contains a minimal vertex cover of size at least $k$. Motivated by the kernelization of MMVC…
In this article, we study the parameterized complexity of the Set Cover problem restricted to semi-ladder-free hypergraphs, a class defined by Fabianski et al. [Proceedings of STACS 2019]. We observe that two algorithms introduced by…
Enumeration kernelization was first proposed by Creignou et al. [TOCS 2017] and was later refined by Golovach et al. [JCSS 2022] into two different variants: fully-polynomial enumeration kernelization and polynomial-delay enumeration…
We study provably effective and efficient data reduction for a class of NP-hard graph modification problems based on vertex degree properties. We show fixed-parameter tractability for NP-hard graph completion (that is, edge addition) cases…
The theory of kernelization can be used to rigorously analyze data reduction for graph coloring problems. Here, the aim is to reduce a q-Coloring input to an equivalent but smaller input whose size is provably bounded in terms of structural…
Graph Burning asks, given a graph $G = (V,E)$ and an integer $k$, whether there exists $(b_{0},\dots,b_{k-1}) \in V^{k}$ such that every vertex in $G$ has distance at most $i$ from some $b_{i}$. This problem is known to be NP-complete even…
In this paper, we study the parameterized complexity of a generalized domination problem called the [${\sigma}, {\rho}$] Dominating Set problem. This problem generalizes a large number of problems including the Minimum Dominating Set…
In this work we study a classic generalization of the Vertex Cover (VC) problem, called the Component Order Connectivity (COC) problem. In COC, given an undirected graph $G$, integers $d \geq 1$ and $k$, the goal is to determine if there is…
Kernelization---a mathematical key concept for provably effective polynomial-time preprocessing of NP-hard problems---plays a central role in parameterized complexity and has triggered an extensive line of research. This is in part due to a…
In parameterized algorithmics, the process of kernelization is defined as a polynomial time algorithm that transforms the instance of a given problem to an equivalent instance of a size that is limited by a function of the parameter. As,…
This paper presents an algorithm, Voted Kernel Regularization , that provides the flexibility of using potentially very complex kernel functions such as predictors based on much higher-degree polynomial kernels, while benefitting from…
A vertex cover on a graph is a set of vertices in which each edge of the graph is adjacent to at least one vertex in the set. The Minimal Vertex Cover (MVC) Problem concerns finding vertex covers with a smallest cardinality. The MVC problem…
For a fixed graph $H$, in the List $H$-Coloring problem, we are given a graph $G$ along with list $L(v) \subseteq V(H)$ for every $v \in V(G)$, and we have to determine if there exists a list homomorphism $\varphi$ from $(G,L)$ to $H$,…
In this paper, we consider the problems of enumerating minimal vertex covers and minimal dominating sets with capacity and/or connectivity constraints. We develop polynomial-delay enumeration algorithms for these problems on bounded-degree…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…