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A defensive $k$-alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at least $k$ more neighbors in $S$ than it has outside of $S$. A defensive $k$-alliance $S$ is called global if it forms a…

Combinatorics · Mathematics 2010-07-29 Ismael G. Yero , Sergio Bermudo , Juan A. Rodriguez-Velazquez , Jose M. Sigarreta

Computing planar orthogonal drawings with the minimum number of bends is one of the most relevant topics in Graph Drawing. The problem is known to be NP-hard, even when we want to test the existence of a rectilinear planar drawing, i.e., an…

Computational Geometry · Computer Science 2023-09-07 Emilio Di Giacomo , Walter Didimo , Giuseppe Liotta , Fabrizio Montecchiani , Giacomo Ortali

Several classical combinatorial problems have been considered and analysed on temporal graphs. Recently, a variant of Vertex Cover on temporal graphs, called MinTimelineCover, has been introduced to summarize timeline activities in social…

Data Structures and Algorithms · Computer Science 2023-07-04 Riccardo Dondi , Manuel Lafond

Steiner Tree Packing (STP) is a notoriously hard problem in classical complexity theory, which is of practical relevance to VLSI circuit design. Previous research has approached this problem by providing heuristic or approximate algorithms.…

Data Structures and Algorithms · Computer Science 2025-05-15 Niko Hastrich , Kirill Simonov

We study the well-established problem of finding an optimal routing of unsplittable flows in a graph. While by now there is an extensive body of work targeting the problem on graph classes such as paths and trees, we aim at using the…

Data Structures and Algorithms · Computer Science 2024-10-23 Robert Ganian , Mathis Rocton , Daniel Unterberger

We investigate the parameterized complexity of the Isometric Path Partition problem when parameterized by the treewidth ($\mathrm{tw}$) of the input graph, arguably one of the most widely studied parameters. Courcelle's theorem shows that…

Data Structures and Algorithms · Computer Science 2025-09-23 Dibyayan Chakraborty , Oscar Defrain , Florent Foucaud , Mathieu Mari , Prafullkumar Tale

Matroids, particularly linear ones, have been a powerful tool in parameterized complexity for algorithms and kernelization. They have sped up or replaced dynamic programming. Delta-matroids generalize matroids by encapsulating structures…

Data Structures and Algorithms · Computer Science 2025-02-20 Eduard Eiben , Tomohiro Koana , Magnus Wahlström

The Metric Dimension problem asks for a minimum-sized resolving set in a given (unweighted, undirected) graph $G$. Here, a set $S \subseteq V(G)$ is resolving if no two distinct vertices of $G$ have the same distance vector to $S$. The…

Data Structures and Algorithms · Computer Science 2021-02-22 Shaohua Li , Marcin Pilipczuk

We consider (closed neighbourhood) packings and their generalization in graphs called limited packings. A vertex set X in a graph G is a k-limited packing if for any vertex $v\in V(G)$, $\left|N[v] \cap X\right| \le k$, where $N[v]$ is the…

Discrete Mathematics · Computer Science 2014-07-08 Andrei Gagarin , Vadim Zverovich

Connected clustering denotes a family of constrained clustering problems in which we are given a distance metric and an undirected connectivity graph $G$ that can be completely unrelated to the metric. The aim is to partition the $n$…

Data Structures and Algorithms · Computer Science 2025-11-25 Jan Eube , Heiko Röglin

We revisit the complexity of the well-studied notion of Additively Separable Hedonic Games (ASHGs). Such games model a basic clustering or coalition formation scenario in which selfish agents are represented by the vertices of an…

Computer Science and Game Theory · Computer Science 2022-02-15 Tesshu Hanaka , Michael Lampis

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…

Data Structures and Algorithms · Computer Science 2023-11-09 Sylvain Guillemot

A metro-line crossing minimization problem is to draw multiple lines on an underlying graph that models stations and rail tracks so that the number of crossings of lines becomes minimum. It has several variations by adding restrictions on…

Data Structures and Algorithms · Computer Science 2013-06-18 Yoshio Okamoto , Yuichi Tatsu , Yushi Uno

We discuss approximability and inapproximability in FPT-time for a large class of subset problems where a feasible solution $S$ is a subset of the input data and the value of $S$ is $|S|$. The class handled encompasses many well-known…

Computational Complexity · Computer Science 2013-10-22 Edouard Bonnet , Vangelis Th. Paschos

We study {\sc Cluster Edge Modification} problems with constraints on the size of the clusters. A graph $G$ is a cluster graph if every connected component of $G$ is a clique. In a typical {\sc Cluster Edge Modification} problem such as the…

Data Structures and Algorithms · Computer Science 2024-09-05 Jayakrishnan Madathil , Kitty Meeks

We consider the problem of transforming a given graph $G_s$ into a desired graph $G_t$ by applying a minimum number primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each…

Distributed, Parallel, and Cluster Computing · Computer Science 2020-09-11 Christian Scheideler , Alexander Setzer

A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…

Data Structures and Algorithms · Computer Science 2023-01-30 Monika Henzinger , Ami Paz , A. R. Sricharan

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

This paper deals with the complexity of some natural graph problems when parametrized by {measures that are restrictions of} clique-width, such as modular-width and neighborhood diversity. The main contribution of this paper is to introduce…

Computational Complexity · Computer Science 2020-02-03 Gennaro Cordasco , Luisa Gargano , Adele Anna Rescigno

There are many classical problems in P whose time complexities have not been improved over the past decades. Recent studies of "Hardness in P" have revealed that, for several of such problems, the current fastest algorithm is the best…

Data Structures and Algorithms · Computer Science 2017-10-24 Yoichi Iwata , Tomoaki Ogasawara , Naoto Ohsaka