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In this paper, we study the Target Set Selection problem from a parameterized complexity perspective. Here for a given graph and a threshold for each vertex, the task is to find a set of vertices (called a target set) which activates the…

Data Structures and Algorithms · Computer Science 2020-08-17 Pavel Dvořák , Dušan Knop , Tomáš Toufar

\textsc{Densest $k$-Subgraph} is the problem to find a vertex subset $S$ of size $k$ such that the number of edges in the subgraph induced by $S$ is maximized. In this paper, we show that \textsc{Densest $k$-Subgraph} is fixed parameter…

Data Structures and Algorithms · Computer Science 2022-07-21 Tesshu Hanaka

We consider parameterised subgraph-counting problems of the following form: given a graph G, how many k-tuples of its vertices have a given property? A number of such problems are known to be #W[1]-complete; here we substantially generalise…

Computational Complexity · Computer Science 2014-09-26 Mark Jerrum , Kitty Meeks

We revisit two well-studied problems, Bounded Degree Vertex Deletion and Defective Coloring, where the input is a graph $G$ and a target degree $\Delta$ and we are asked either to edit or partition the graph so that the maximum degree…

Data Structures and Algorithms · Computer Science 2024-05-07 Michael Lampis , Manolis Vasilakis

Hub Covering Problems arise in various practical domains, such as urban planning, cargo delivery systems, airline networks, telecommunication network design, and e-mobility. The task is to select a set of hubs that enable tours between…

Discrete Mathematics · Computer Science 2025-03-05 Niklas Jost

The Firefighting problem is defined as follows. At time $t=0$, a fire breaks out at a vertex of a graph. At each time step $t \geq 0$, a firefighter permanently defends (protects) an unburned vertex, and the fire then spread to all…

Data Structures and Algorithms · Computer Science 2017-11-29 Bireswar Das , Murali Krishna Enduri , Neeldhara Misra , I. Vinod Reddy

The VertexCover problem is proven to be computationally hard in different ways: It is NP-complete to find an optimal solution and even NP-hard to find an approximation with reasonable factors. In contrast, recent experiments suggest that on…

Data Structures and Algorithms · Computer Science 2020-02-20 Thomas Bläsius , Philipp Fischbeck , Tobias Friedrich , Maximilian Katzmann

In this paper we study the generalized vertex cover problem (GVC), which is a generalization of various well studied combinatorial optimization problems. GVC is shown to be equivalent to the unconstrained binary quadratic programming…

Computational Complexity · Computer Science 2017-08-15 Pooja Pandey , Abraham P. Punnen

This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…

Data Structures and Algorithms · Computer Science 2018-02-21 Hao-Ting Wei , Wing-Kai Hon , Paul Horn , Chung-Shou Liao , Kunihiko Sadakane

We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…

Discrete Mathematics · Computer Science 2011-01-27 Ken-ichi Kawarabayashi , Mikkel Thorup

We introduce and study two natural generalizations of the Connected VertexCover (VC) problem: the $p$-Edge-Connected and $p$-Vertex-Connected VC problem (where $p \geq 2$ is a fixed integer). Like Connected VC, both new VC problems are FPT,…

Data Structures and Algorithms · Computer Science 2022-08-23 Carl Einarson , Gregory Gutin , Bart M. P. Jansen , Diptapriyo Majumdar , Magnus Wahlstrom

We present a method to obtain upper bounds on covering numbers. As applications of this method, we reprove and generalize results of Rogers on economically covering Euclidean $n$-space with translates of a convex body, or more generally,…

Metric Geometry · Mathematics 2015-10-12 Márton Naszódi

We analyze the computational complexity of the following computational problems called Bounded-Density Edge Deletion and Bounded-Density Vertex Deletion: Given a graph $G$, a budget $k$ and a target density $\tau_\rho$, are there $k$ edges…

Data Structures and Algorithms · Computer Science 2024-04-15 Cristina Bazgan , André Nichterlein , Sofia Vazquez Alferez

Vertex deletion problems for graphs are studied intensely in classical and parameterized complexity theory. They ask whether we can delete at most k vertices from an input graph such that the resulting graph has a certain property.…

Logic in Computer Science · Computer Science 2024-06-27 Max Bannach , Florian Chudigiewitsch , Till Tantau

The article studies edge coverage for control flow graphs extended with explicit constraints. Achieving a given level of white-box coverage for a given code is a classic problem in software testing. We focus on designing test sets that…

Computational Complexity · Computer Science 2026-02-24 Jakub Ruszil , Artur Polański , Adam Roman , Jakub Zelek

We study a variant of Set Cover where each element of the universe has some demand that determines how many times the element needs to be covered. Moreover, we examine two generalizations of this problem when a set can be included multiple…

Data Structures and Algorithms · Computer Science 2021-04-21 Niclas Boehmer , Robert Bredereck , Dušan Knop , Junjie Luo

We prove that the Minimum Distance Problem (MDP) on linear codes over any fixed finite field and parameterized by the input distance bound is W[1]-hard to approximate within any constant factor. We also prove analogous results for the…

Computational Complexity · Computer Science 2024-02-28 Huck Bennett , Mahdi Cheraghchi , Venkatesan Guruswami , João Ribeiro

Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…

Computational Complexity · Computer Science 2015-06-01 Kitty Meeks

The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a…

Computational Complexity · Computer Science 2017-03-21 Yijia Chen , Martin Grohe , Bingkai Lin

We study the model checking problem of an extended $\mathsf{MSO}$ with local and global cardinality constraints, called $\mathsf{MSO}^{\mathsf{GL}}_{\mathsf{Lin}}$, introduced recently by Knop, Kouteck\'{y}, Masa\v{r}\'{i}k, and Toufar…

Data Structures and Algorithms · Computer Science 2023-10-17 Tatsuya Gima , Yota Otachi