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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

In the Disjoint Paths problem, the input consists of an $n$-vertex graph $G$ and a collection of $k$ vertex pairs, $\{(s_i,t_i)\}_{i=1}^k$, and the objective is to determine whether there exists a collection $\{P_i\}_{i=1}^k$ of $k$…

Data Structures and Algorithms · Computer Science 2020-08-20 Daniel Lokshtanov , Saket Saurabh , Meirav Zehavi

\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 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 carry out a systematic study of a natural covering problem, used for identification across several areas, in the realm of parameterized complexity. In the {\sc Test Cover} problem we are given a set $[n]=\{1,...,n\}$ of items together…

Data Structures and Algorithms · Computer Science 2012-12-04 R. Crowston , G. Gutin , M. Jones , S. Saurabh , A. Yeo

Given a graph $G=(V,E)$, a set $\mathcal{F}$ of forbidden subgraphs, we study $\mathcal{F}$-Free Edge Deletion, where the goal is to remove minimum number of edges such that the resulting graph does not contain any $F\in \mathcal{F}$ as a…

Data Structures and Algorithms · Computer Science 2021-02-12 Ajinkya Gaikwad , Soumen Maity

Given an orthogonal connected arrangement of line-segments, Minimum Corridor Guarding(MCG) problem asks for an optimal tree/closed walk such that, if a guard moves through the tree/closed walk, all the line-segments are visited by the…

Computational Geometry · Computer Science 2022-03-30 Remi Raman , R Subashini , Subhasree Methirumangalath

For a graph $G$, a subset $S \subseteq V(G)$ is called a \emph{resolving set} if for any two vertices $u,v \in V(G)$, there exists a vertex $w \in S$ such that $d(w,u) \neq d(w,v)$. The {\sc Metric Dimension} problem takes as input a graph…

Discrete Mathematics · Computer Science 2023-06-08 Esther Galby , Liana Khazaliya , Fionn Mc Inerney , Roohani Sharma , Prafullkumar Tale

We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…

Artificial Intelligence · Computer Science 2009-03-04 Christian Bessiere , Emmanuel Hebrard , Brahim Hnich , Zeynep Kiziltan , Toby Walsh

The recently introduced graph parameter tree-cut width plays a similar role with respect to immersions as the graph parameter treewidth plays with respect to minors. In this paper, we provide the first algorithmic applications of tree-cut…

Data Structures and Algorithms · Computer Science 2022-06-03 Robert Ganian , Eun Jung Kim , Stefan Szeider

Given $k$ input graphs $G_1, \dots ,G_k$, where each pair $G_i$, $G_j$ with $i \neq j$ shares the same graph $G$, the problem Simultaneous Embedding With Fixed Edges (SEFE) asks whether there exists a planar drawing for each input graph…

Data Structures and Algorithms · Computer Science 2025-05-01 Simon D. Fink , Matthias Pfretzschner , Ignaz Rutter

Parallel parameterized complexity theory studies how fixed-parameter tractable (fpt) problems can be solved in parallel. Previous theoretical work focused on parallel algorithms that are very fast in principle, but did not take into account…

Data Structures and Algorithms · Computer Science 2019-02-21 Max Bannach , Malte Skambath , Till Tantau

We study a variant of Min Cost Flow in which the flow needs to be connected. Specifically, in the Connected Flow problem one is given a directed graph $G$, along with a set of demand vertices $D \subseteq V(G)$ with demands $\mathsf{dem}: D…

Data Structures and Algorithms · Computer Science 2021-07-21 Isja Mannens , Jesper Nederlof , Céline Swennenhuis , Krisztina Szilágyi

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

We study the Induced $H$ Partition problem from the parameterized complexity point of view. In the Induced $H$ Partition problem the task is to partition vertices of a graph $G$ into sets $V_1,V_2,\dots,V_n$ such that the graph $H$ is…

Discrete Mathematics · Computer Science 2016-03-11 Dušan Knop

We study the parameterized complexity of the graph isomorphism problem when parameterized by width parameters related to tree decompositions. We apply the following technique to obtain fixed-parameter tractability for such parameters. We…

Discrete Mathematics · Computer Science 2014-03-31 Yota Otachi , Pascal Schweitzer

We show that the following two problems are fixed-parameter tractable with parameter k: testing whether a connected n-vertex graph with m edges has a square root with at most n-1+k edges and testing whether such a graph has a square root…

Data Structures and Algorithms · Computer Science 2013-10-22 Manfred Cochefert , Jean-François Couturier , Petr A. Golovach , Dieter Kratsch , Daniël Paulusma

We study the parameterized complexity of the directed variant of the classical {\sc Steiner Tree} problem on various classes of directed sparse graphs. While the parameterized complexity of {\sc Steiner Tree} parameterized by the number of…

Data Structures and Algorithms · Computer Science 2012-10-02 Mark Jones , Daniel Lokshtanov , M. S. Ramanujan , Saket Saurabh , Ondřej Suchý

We consider the \textsc{Steiner Orientation} problem, where we are given as input a mixed graph $G=(V,E,A)$ and a set of $k$ demand pairs $(s_i,t_i)$, $i\in[k]$. The goal is to orient the undirected edges of $G$ in a way that the resulting…

Data Structures and Algorithms · Computer Science 2025-07-30 Tesshu Hanaka , Michael Lampis , Nikolaos Melissinos , Edouard Nemery , Hirotaka Ono , Manolis Vasilakis

Problems related to finding induced subgraphs satisfying given properties form one of the most studied areas within graph algorithms. Such problems have given rise to breakthrough results and led to development of new techniques both within…

Data Structures and Algorithms · Computer Science 2017-10-31 Petr A. Golovach , Pinar Heggernes , Paloma Lima , Pedro Montealegre