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Capacitated Vertex Cover is the hard-capacitated variant of Vertex Cover: given a graph, a capacity for every vertex, and an integer $k$, the task is to select at most $k$ vertices that cover all edges and assign each edge to one of its…

Data Structures and Algorithms · Computer Science 2026-04-22 Michael Lampis , Manolis Vasilakis

We study a recently introduced generalization of the Vertex Cover (VC) problem, called Power Vertex Cover (PVC). In this problem, each edge of the input graph is supplied with a positive integer demand. A solution is an assignment of…

Data Structures and Algorithms · Computer Science 2023-06-22 Eric Angel , Evripidis Bampis , Bruno Escoffier , Michael Lampis

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…

Computational Complexity · Computer Science 2017-08-28 Henning Fernau , Till Fluschnik , Danny Hermelin , Andreas Krebs , Hendrik Molter , Rolf Niedermeier

The Identifying Code (IC) problem seeks a vertex subset whose intersection with every vertex's closed neighborhood is unique, enabling fault detection in multiprocessor systems and practical uses in identity verification, environmental…

Computational Complexity · Computer Science 2025-11-27 Aritra Banik , Praneet Kumar Patra , Adele Anna Rescigno , Abhishek Sahu

We investigate the classical and distributed complexity of \emph{$k$-partial $c$-coloring} where $c=k$, a natural generalization of Brooks' theorem where each vertex should be colored from the palette $\{1,\ldots,c\} = \{1,\ldots,k\}$ such…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-08-27 Jan Bok , Avinandan Das , Anna Gujgiczer , Nikola Jedličková

We consider problems where the input is a set of points in the plane and an integer $k$, and the task is to find a subset $S$ of the input points of size $k$ such that $S$ satisfies some property. We focus on properties that depend only on…

Computational Geometry · Computer Science 2018-08-08 David Eppstein , Daniel Lokshtanov

A vertex-subset graph problem $Q$ defines which subsets of the vertices of an input graph are feasible solutions. The reconfiguration version of a vertex-subset problem $Q$ asks whether it is possible to transform one feasible solution for…

Computational Complexity · Computer Science 2014-09-30 Amer E. Mouawad , Naomi Nishimura , Venkatesh Raman , Marcin Wrochna

In the $(k,h)$-SetCover problem, we are given a collection $\mathcal{S}$ of sets over a universe $U$, and the goal is to distinguish between the case that $\mathcal{S}$ contains $k$ sets which cover $U$, from the case that at least $h$ sets…

Computational Complexity · Computer Science 2020-09-08 Karthik C. S. , Inbal Livni-Navon

A graph $G$ covers a graph $H$ if there exists a locally bijective homomorphism from $G$ to $H$. We deal with regular covers where this homomorphism is prescribed by the action of a semiregular subgroup of $\textrm{Aut}(G)$. We study…

Discrete Mathematics · Computer Science 2017-01-31 Jiří Fiala , Pavel Klavík , Jan Kratochvíl , Roman Nedela

We investigate the parameterized complexity of finding subgraphs with hereditary properties on graphs belonging to a hereditary graph class. Given a graph $G$, a non-trivial hereditary property $\Pi$ and an integer parameter $k$, the…

Data Structures and Algorithms · Computer Science 2021-01-26 David Eppstein , Siddharth Gupta , Elham Havvaei

Let $X,Y$ be finite sets, $r,s,h, \lambda \in \mathbb{N}$ with $s\geq r, X\subsetneq Y$. By $\lambda \binom{X}{h}$ we mean the collection of all $h$-subsets of $X$ where each subset occurs $\lambda$ times. A coloring of…

Combinatorics · Mathematics 2020-09-23 Amin Bahmanian , Sadegheh Haghshenas

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…

Data Structures and Algorithms · Computer Science 2016-11-07 Daniel Lokshtanov , Fahad Panolan , M. S. Ramanujan , Saket Saurabh

A Ranking r-Constraint Satisfaction Problem (ranking r-CSP) consists of a ground set of vertices V, an arity r >= 2, a parameter k and a constraint system c, where c is a function which maps rankings of r-sized subsets of V to {0,1}. The…

Discrete Mathematics · Computer Science 2012-10-26 Anthony Perez

An $\ell$-page stack layout (also known as an $\ell$-page book embedding) of a graph is a linear order of the vertex set together with a partition of the edge set into $\ell$ stacks (or pages), such that the endpoints of no two edges on the…

Computational Geometry · Computer Science 2024-09-05 Thomas Depian , Simon D. Fink , Robert Ganian , Martin Nöllenburg

We investigate the parameterized complexity of Maximum Exposure Problem (MEP). Given a range space (R, P) where R is the set of ranges containing a set P of points, and an integer k, MEP asks for k ranges which on removal results in the…

Computational Geometry · Computer Science 2022-03-23 Remi Raman , Shahin John J S , R Subashini , Subhasree Methirumangalath

We study the NP-hard graph problem Collapsed k-Core where, given an undirected graph G and integers b, x, and k, we are asked to remove b vertices such that the k-core of remaining graph, that is, the (uniquely determined) largest induced…

Discrete Mathematics · Computer Science 2018-06-01 Junjie Luo , Hendrik Molter , Ondrej Suchy

We revisit connectivity-constrained coverage through a unifying model, Partial Connected Red-Blue Dominating Set. Given a red-blue bipartite graph $G$ and an auxiliary connectivity graph $G_{conn}$ on red vertices, and integers $k, t$, the…

Data Structures and Algorithms · Computer Science 2026-01-14 Tanmay Inamdar , Satyabrata Jana , Madhumita Kundu , Daniel Lokshtanov , Saket Saurabh , Meirav Zehavi

For fixed integers $r,\ell \geq 0$, a graph $G$ is called an {\em $(r,\ell)$-graph} if the vertex set $V(G)$ can be partitioned into $r$ independent sets and $\ell$ cliques. This brings us to the following natural parameterized questions:…

Computational Complexity · Computer Science 2015-05-05 Sudeshna Kolay , Fahad Panolan

The notion of graph covers (also referred to as locally bijective homomorphisms) plays an important role in topological graph theory and has found its computer science applications in models of local computation. For a fixed target graph…

Discrete Mathematics · Computer Science 2025-02-28 Jan Bok , Jiří Fiala , Nikola Jedličková , Jan Kratochvíl , Micheala Seifrtová

We study the parameterized complexity of the following fundamental geometric problems with respect to the dimension $d$: i) Given $n$ points in $\Rd$, compute their minimum enclosing cylinder. ii) Given two $n$-point sets in $\Rd$, decide…

Computational Geometry · Computer Science 2015-02-18 Panos Giannopoulos , Christian Knauer , Gunter Rote , Daniel Werner