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We consider the problem of finding a 1-planar drawing for a general graph, where a 1-planar drawing is a drawing in which each edge participates in at most one crossing. Since this problem is known to be NP-hard we investigate the…

Data Structures and Algorithms · Computer Science 2018-12-18 Michael J. Bannister , Sergio Cabello , David Eppstein

Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More…

Data Structures and Algorithms · Computer Science 2017-10-19 David Coudert , Guillaume Ducoffe , Alexandru Popa

We give an analog of the Myhill-Nerode methods from formal language theory for hypergraphs and use it to derive the following results for two NP-hard hypergraph problems: * We provide an algorithm for testing whether a hypergraph has…

Discrete Mathematics · Computer Science 2016-01-12 René van Bevern , Rodney G. Downey , Michael R. Fellows , Serge Gaspers , Frances A. Rosamond

A clique coloring of a graph is an assignment of colors to its vertices such that no maximal clique is monochromatic. We initiate the study of structural parameterizations of the Clique Coloring problem which asks whether a given graph has…

Data Structures and Algorithms · Computer Science 2020-05-12 Lars Jaffke , Paloma T. Lima , Geevarghese Philip

We consider a bi-criteria generalization of the pathwidth problem, where, for given integers $k,l$ and a graph $G$, we ask whether there exists a path decomposition $\cP$ of $G$ such that the width of $\cP$ is at most $k$ and the number of…

Data Structures and Algorithms · Computer Science 2021-03-05 Dariusz Dereniowski , Wieslaw Kubiak , Yori Zwols

We continue and extend previous work on the parameterized complexity analysis of the NP-hard Stable Roommates with Ties and Incomplete Lists problem, thereby strengthening earlier results both on the side of parameterized hardness as well…

Computational Complexity · Computer Science 2021-03-09 Robert Bredereck , Klaus Heeger , Dušan Knop , Rolf Niedermeier

We consider the well-studied problem of finding a spanning tree with minimum average distance between vertex pairs (called a MAD tree). This is a classic network design problem which is known to be NP-hard. While approximation algorithms…

Data Structures and Algorithms · Computer Science 2026-04-01 Tom-Lukas Breitkopf , Vincent Froese , Anton Herrmann , André Nichterlein , Camille Richer

Due to their importance in practice, dominating set problems in graphs have been greatly studied in past and different formulations of these problems are presented in literature. This paper's focus is on two problems: weakly convex…

Optimization and Control · Mathematics 2019-04-05 Jozef Kratica , Vladimir Filipovic , Dragan Matic , Aleksandar Kartelj

We study the power of the bounded-width consistency algorithm in the context of the fixed-template Promise Constraint Satisfaction Problem (PCSP). Our main technical finding is that the template of every PCSP that is solvable in bounded…

Computational Complexity · Computer Science 2021-07-14 Albert Atserias , Víctor Dalmau

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the…

Computational Complexity · Computer Science 2016-05-17 Archontia C. Giannopoulou , George B. Mertzios

The concept of generalized domination unifies well-known variants of domination-like and independence problems, such as Dominating Set, Independent Set, Perfect Code, etc. A generalized domination (also called $[\sigma,\rho]$-Dominating…

Computational Complexity · Computer Science 2014-04-04 Mathieu Chapelle

Integer Linear Programming (ILP) can be seen as the archetypical problem for NP-complete optimization problems, and a wide range of problems in artificial intelligence are solved in practice via a translation to ILP. Despite its huge range…

Data Structures and Algorithms · Computer Science 2018-09-05 Robert Ganian , Sebastian Ordyniak

In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…

Data Structures and Algorithms · Computer Science 2012-12-18 Mugurel Ionut Andreica

In the presented paper we study the Length-Bounded Cut problem for special graph classes as well as from a parameterized-complexity viewpoint. Here, we are given a graph $G$, two vertices $s$ and $t$, and positive integers $\beta$ and…

Data Structures and Algorithms · Computer Science 2019-10-09 Matthias Bentert , Klaus Heeger , Dušan Knop

We study integer linear programs (ILP) of the form $\min\{c^\top x\ \vert\ Ax=b,l\le x\le u,x\in\mathbb Z^n\}$ and analyze their parameterized complexity with respect to their distance to the generalized matching problem, following the…

Computational Complexity · Computer Science 2025-10-20 Alexandra Lassota , Koen Ligthart

Parameterized complexity seeks to use input structure to obtain faster algorithms for NP-hard problems. This has been most successful for graphs of low treewidth: Many problems admit fast algorithms relative to treewidth and many of them…

Computational Complexity · Computer Science 2022-12-20 Falko Hegerfeld , Stefan Kratsch

For any $\varepsilon > 0$, we give a polynomial-time $n^\varepsilon$-approximation algorithm for Max Independent Set in graphs of bounded twin-width given with an $O(1)$-sequence. This result is derived from the following time-approximation…

Data Structures and Algorithms · Computer Science 2022-09-27 Pierre Bergé , Édouard Bonnet , Hugues Déprés , Rémi Watrigant

Partial vertex cover and partial dominating set are two well-investigated optimization problems. While they are $\rm W[1]$-hard on general graphs, they have been shown to be fixed-parameter tractable on many sparse graph classes, including…

Data Structures and Algorithms · Computer Science 2025-07-01 Jakub Balabán , Daniel Mock , Peter Rossmanith

We complement the recent algorithmic result that Feedback Vertex Set is XP-time solvable parameterized by the mim-width of a given branch decomposition of the input graph [3] by showing that the problem is W[1]-hard in this…

Computational Complexity · Computer Science 2017-11-15 Lars Jaffke , O-joung Kwon , Jan Arne Telle

We introduce an extension of decision problems called resiliency problems. In resiliency problems, the goal is to decide whether an instance remains positive after any (appropriately defined) perturbation has been applied to it. To tackle…

Data Structures and Algorithms · Computer Science 2018-05-04 Jason Crampton , Gregory Gutin , Martin Koutecký , Rémi Watrigant