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Given an undirected graph $G=(V,E)$ and an integer $\ell$, the Eccentricity Shortest Path (ESP) asks to find a shortest path $P$ such that for every vertex $v\in V(G)$, there is a vertex $w\in P$ such that $d_G(v,w)\leq \ell$, where…

Data Structures and Algorithms · Computer Science 2023-04-07 Sriram Bhyravarapu , Satyabrata Jana , Lawqueen Kanesh , Saket Saurabh , Shaily Verma

A well-studied continuous model of graphs considers each edge as a continuous unit-length interval of points. In the problem $\delta$-Tour defined within this model, the objective to find a shortest tour that comes within a distance of…

Data Structures and Algorithms · Computer Science 2025-02-27 Fabian Frei , Ahmed Ghazy , Tim A. Hartmann , Florian Hörsch , Dániel Marx

The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…

Computational Geometry · Computer Science 2023-02-21 Sujoy Bhore , Robert Ganian , Liana Khazaliya , Fabrizio Montecchiani , Martin Nöllenburg

In the maximum satisfiability problem (MAX-SAT) we are given a propositional formula in conjunctive normal form and have to find an assignment that satisfies as many clauses as possible. We study the parallel parameterized complexity of…

Computational Complexity · Computer Science 2022-06-06 Max Bannach , Malte Skambath , Till Tantau

Given a graph $G = (V, E)$, a non-empty set $S \subseteq V$ is a defensive alliance, if for every vertex $v \in S$, the majority of its closed neighbours are in $S$, that is, $|N_G[v] \cap S| \geq |N_G[v] \setminus S|$. The decision version…

Data Structures and Algorithms · Computer Science 2023-07-20 Sangam Balchandar Reddy , Anjeneya Swami Kare

In the continuous 1.5-dimensional terrain guarding problem we are given an $x$-monotone chain (the \emph{terrain} $T$) and ask for the minimum number of point guards (located anywhere on $T$), such that all points of $T$ are covered by at…

Computational Geometry · Computer Science 2014-07-29 Stephan Friedrichs , Michael Hemmer , Christiane Schmidt

A prototypical graph problem is centered around a graph-theoretic property for a set of vertices and a solution to it is a set of vertices for which the desired property holds. The task is to decide whether, in the given graph, there exists…

Computational Complexity · Computer Science 2020-06-11 Dušan Knop , Tomáš Masařík , Tomáš Toufar

Matroid interdiction problems are well-researched in the field of combinatorial optimization. In the matroid $\ell$-interdiction problem, an interdiction strategy removes a subset of cardinality $\ell$ from the matroid's ground set. The…

Combinatorics · Mathematics 2025-11-17 Nils Hausbrandt , Levin Nemesch , Stefan Ruzika

The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…

Data Structures and Algorithms · Computer Science 2022-12-22 Kitty Meeks , Fiona Skerman

Parameterized Inapproximability Hypothesis (PIH) is a central question in the field of parameterized complexity. PIH asserts that given as input a 2-CSP on $k$ variables and alphabet size $n$, it is W[1]-hard parameterized by $k$ to…

Computational Complexity · Computer Science 2024-07-15 Karthik C. S. , Euiwoong Lee , Pasin Manurangsi

We consider the problems ZERO EXTENSION and METRIC LABELLING under the paradigm of parameterized complexity. These are natural, well-studied problems with important applications, but have previously not received much attention from…

Data Structures and Algorithms · Computer Science 2018-02-19 Felix Reidl , Magnus Wahlström

We study the algorithmic complexity of partitioning the vertex set of a given (di)graph into a small number of paths. The Path Partition problem (PP) has been studied extensively, as it includes Hamiltonian Path as a special case. The…

Data Structures and Algorithms · Computer Science 2024-12-24 Henning Fernau , Florent Foucaud , Kevin Mann , Utkarsh Padariya , Rajath Rao K. N

Parameterized analysis provides powerful mechanisms for obtaining fine-grained insights into different types of algorithms. In this work, we combine this field with evolutionary algorithms and provide parameterized complexity analysis of…

Combinatorics · Mathematics 2023-03-22 Samuel Baguley , Tobias Friedrich , Aneta Neumann , Frank Neumann , Marcus Pappik , Ziena Zeif

Treewidth (tw) is an important parameter that, when bounded, yields tractability for many problems. For example, graph problems expressible in Monadic Second Order (MSO) logic and QUANTIFIED SAT or, more generally, QUANTIFIED CSP, are FPT…

Computational Complexity · Computer Science 2025-03-18 Florent Foucaud , Esther Galby , Liana Khazaliya , Shaohua Li , Fionn Mc Inerney , Roohani Sharma , Prafullkumar Tale

Parameterized algorithms are a very useful tool for dealing with NP-hard problems on graphs. Yet, to properly utilize parameterized algorithms it is necessary to choose the right parameter based on the type of problem and properties of the…

Data Structures and Algorithms · Computer Science 2012-01-18 Robert Ganian

The Virtual Network Embedding Problem (VNEP) considers the efficient allocation of resources distributed in a substrate network to a set of request networks. Many existing works discuss either heuristics or exact algorithms, resulting in a…

Networking and Internet Architecture · Computer Science 2018-10-29 Elias Döhne

We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…

Data Structures and Algorithms · Computer Science 2021-07-19 Julián Mestre , Sergey Pupyrev , Seeun William Umboh

We study a generalization of the Set Cover problem called the \emph{Partial Set Cover} in the context of geometric set systems. The input to this problem is a set system $(X, \mathcal{S})$, where $X$ is a set of elements and $\mathcal{S}$…

Computational Geometry · Computer Science 2017-12-13 Tanmay Inamdar , Kasturi Varadarajan

Finding a cycle of lowest weight that represents a homology class in a simplicial complex is known as homology localization (HL). Here we address this NP-complete problem using parameterized complexity theory. We show that it is W[1]-hard…

Computational Geometry · Computer Science 2020-12-01 Nello Blaser , Erlend Raa Vågset

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