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The dichotomy conjecture for the parameterized embedding problem states that the problem of deciding whether a given graph $G$ from some class $K$ of "pattern graphs" can be embedded into a given graph $H$ (that is, is isomorphic to a…

Computational Complexity · Computer Science 2017-03-21 Yijia Chen , Martin Grohe , Bingkai Lin

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

Exact pattern matching in labeled graphs is the problem of searching paths of a graph $G=(V,E)$ that spell the same string as the given pattern $P[1..m]$. This basic problem can be found at the heart of more complex operations on variation…

Computational Complexity · Computer Science 2019-02-12 Massimo Equi , Roberto Grossi , Alexandru I. Tomescu , Veli Mäkinen

Given a set of obstacles and two points, is there a path between the two points that does not cross more than $k$ different obstacles? This is a fundamental problem that has undergone a tremendous amount of work. It is known to be NP-hard,…

Computational Geometry · Computer Science 2017-12-13 Eduard Eiben , Iyad Kanj

Let $G$ be a bipartite graph with bipartition $(X,Y)$. Inspired by a hypergraph problem, we seek an upper bound on the number of disjoint paths needed to cover all the vertices of $X$. We conjecture that a Hall-type sufficient condition…

Combinatorics · Mathematics 2023-10-10 Mikhail Lavrov , Jennifer Vandenbussche

The MULTICUT problem, given a graph G, a set of terminal pairs T={(s_i,t_i) | 1 <= i <= r} and an integer p, asks whether one can find a cutset consisting of at most p non-terminal vertices that separates all the terminal pairs, i.e., after…

Data Structures and Algorithms · Computer Science 2012-02-28 Stefan Kratsch , Marcin Pilipczuk , Michał Pilipczuk , Magnus Wahlström

We examine the problem of maximizing the reachability of a given source in temporal graphs that are given as the union of k temporal paths, i.e., every given path is a sequence of edges with strictly increasing labels that denote…

Data Structures and Algorithms · Computer Science 2026-05-13 Argyrios Deligkas , Michelle Döring , Eduard Eiben , George Skretas , Georg Tennigkeit

The Disjoint Paths Problem asks, given a graph $G$ and a set of pairs of terminals $(s_{1},t_{1}),\ldots,(s_{k},t_{k})$, whether there is a collection of $k$ pairwise vertex-disjoint paths linking $s_{i}$ and $t_{i}$, for $i=1,\ldots,k.$ In…

In the Maximum Connectivity Improvement (MCI) problem, we are given a directed graph $G=(V,E)$ and an integer $B$ and we are asked to find $B$ new edges to be added to $G$ in order to maximize the number of connected pairs of vertices in…

Discrete Mathematics · Computer Science 2019-04-30 Federico Corò , Gianlorenzo D'Angelo , Vahan Mkrtchyan

We show that the dominating set problem parameterized by solution size is fixed-parameter tractable (FPT) in graphs that do not contain the claw (K(1,3)), the complete bipartite graph on four vertices where the two parts have one and three…

Data Structures and Algorithms · Computer Science 2015-03-17 Marek Cygan , Geevarghese Philip , Marcin Pilipczuk , Michał Pilipczuk , Jakub Onufry Wojtaszczyk

We devise a constant-factor approximation algorithm for the maximization version of the edge-disjoint paths problem if the supply graph together with the demand edges form a planar graph. By planar duality this is equivalent to packing cuts…

Data Structures and Algorithms · Computer Science 2021-12-14 Chien-Chung Huang , Mathieu Mari , Claire Mathieu , Kevin Schewior , Jens Vygen

We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as…

Data Structures and Algorithms · Computer Science 2022-07-18 Fedor V. Fomin , Petr A. Golovach , Tuukka Korhonen , Kirill Simonov , Giannos Stamoulis

In the Directed Steiner Network problem, the input is a directed graph G, a subset T of k vertices of G called the terminals, and a demand graph D on T. The task is to find a subgraph H of G with the minimum number of edges such that for…

Data Structures and Algorithms · Computer Science 2022-08-15 Esther Galby , Sandor Kisfaludi-Bak , Daniel Marx , Roohani Sharma

For a class $\mathcal{H}$ of graphs, #Sub$(\mathcal{H})$ is the counting problem that, given a graph $H\in \mathcal{H}$ and an arbitrary graph $G$, asks for the number of subgraphs of $G$ isomorphic to $H$. It is known that if $\mathcal{H}$…

Computational Complexity · Computer Science 2014-07-11 Radu Curticapean , Dániel Marx

Given a graph $G$ and a parameter $k$, the $k$-biclique problem asks whether $G$ contains a complete bipartite subgraph $K_{k,k}$. This is the most easily stated problem on graphs whose parameterized complexity is still unknown. We provide…

Computational Complexity · Computer Science 2019-06-11 Bingkai Lin

A graph $G$ has maximal local edge-connectivity $k$ if the maximum number of edge-disjoint paths between every pair of distinct vertices $x$ and $y$ is at most $k$. We prove Brooks-type theorems for $k$-connected graphs with maximal local…

Combinatorics · Mathematics 2022-03-07 Pierre Aboulker , Nick Brettell , Frédéric Havet , Dániel Marx , Nicolas Trotignon

Bhawalkar, Kleinberg, Lewi, Roughgarden, and Sharma [ICALP 2012] introduced the Anchored k-Core problem, where the task is for a given graph G and integers b, k, and p to find an induced subgraph H with at least p vertices (the core) such…

Data Structures and Algorithms · Computer Science 2013-09-18 Rajesh Chitnis , Fedor V. Fomin , Petr A. Golovach

We investigate the terminal-pairibility problem in the case when the base graph is a complete bipartite graph, and the demand graph is also bipartite with the same color classes. We improve the lower bound on maximum value of $\Delta(D)$…

Combinatorics · Mathematics 2020-04-22 Lucas Colucci , Péter L. Erdős , Ervin Győri , Tamás Róbert Mezei

Reconfigurable optical topologies promise to improve the performance in datacenters by dynamically optimizing the physical network in a demand-aware manner. State-of-the-art optical technologies allow to establish and update direct…

Data Structures and Algorithms · Computer Science 2023-01-18 Kathrin Hanauer , Monika Henzinger , Stefan Schmid , Jonathan Trummer

We study the Short Path Packing problem which asks, given a graph $G$, integers $k$ and $\ell$, and vertices $s$ and $t$, whether there exist $k$ pairwise internally vertex-disjoint $s$-$t$ paths of length at most $\ell$. The problem has…

Data Structures and Algorithms · Computer Science 2024-04-17 Michael Kiran Huber