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Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer k, find a set of at least k pairwise non-adjacent…

Discrete Mathematics · Computer Science 2016-01-12 René van Bevern , Matthias Mnich , Rolf Niedermeier , Mathias Weller

We investigate the computational complexity of finding temporally disjoint paths or walks in temporal graphs. There, the edge set changes over discrete time steps and a temporal path (resp. walk) uses edges that appear at monotonically…

Data Structures and Algorithms · Computer Science 2021-05-25 Nina Klobas , George B. Mertzios , Hendrik Molter , Rolf Niedermeier , Philipp Zschoche

We study a natural variant of scheduling that we call \emph{partial scheduling}: In this variant an instance of a scheduling problem along with an integer $k$ is given and one seeks an optimal schedule where not all, but only $k$ jobs, have…

Data Structures and Algorithms · Computer Science 2020-10-02 Jesper Nederlof , Céline Swennenhuis

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

We study the problem of non-preemptively scheduling $n$ jobs, each job $j$ with a release time $t_j$, a deadline $d_j$, and a processing time $p_j$, on $m$ parallel identical machines. Cieliebak et al. (2004) considered the two constraints…

Data Structures and Algorithms · Computer Science 2017-05-25 René van Bevern , Rolf Niedermeier , Ondřej Suchý

Evaluation of regular path queries (RPQs) is a central problem in graph databases. We investigate the corresponding enumeration problem, that is, given a graph and an RPQ, enumerate all paths in the graph that match the RPQ. We consider…

Databases · Computer Science 2017-10-09 Wim Martens , Tina Trautner

A two-dimensional grid with dots is called a \emph{configuration with distinct differences} if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many…

Combinatorics · Mathematics 2009-10-08 Simon R. Blackburn , Tuvi Etzion , Keith M. Martin , Maura B. Paterson

We consider the problem of decomposing a given (di)graph into paths of length 2 with the additional restriction that no two such paths may have more than one vertex in common. We establish its NP-hardness by a reduction from 3-SAT,…

Discrete Mathematics · Computer Science 2019-07-12 Annika Thome , Matthias Walter

The embedding problem is to decide, given an ordered pair of structures, whether or not there is an injective homomorphism from the first structure to the second. We study this problem using an established perspective in parameterized…

Computational Complexity · Computer Science 2017-01-09 Hubie Chen , Moritz Müller

We propose a novel way of generalizing the class of interval graphs, via a graph width parameter called the simultaneous interval number. This parameter is related to the simultaneous representation problem for interval graphs and defined…

Discrete Mathematics · Computer Science 2024-04-17 Jesse Beisegel , Nina Chiarelli , Ekkehard Köhler , Martin Milanič , Peter Muršič , Robert Scheffler

We study the parametrized complexity of fundamental relations between multidimensional subshifts, such as equality, conjugacy, inclusion, and embedding, for subshifts of finite type (SFTs) and effective subshifts. We build on previous work…

Dynamical Systems · Mathematics 2026-02-16 Nicanor Carrasco-Vargas , Benjamin Hellouin de Menibus , Rémi Pallen

In the Maximum Common Induced Subgraph problem (henceforth MCIS), given two graphs $G_1$ and $G_2$, one looks for a graph with the maximum number of vertices being both an induced subgraph of $G_1$ and $G_2$. MCIS is among the most studied…

Data Structures and Algorithms · Computer Science 2017-02-23 Faisal N. Abu-Khzam , Édouard Bonnet , Florian Sikora

The weighted $\mathcal{T}$-free $2$-matching problem is the following problem: given an undirected graph $G$, a weight function on its edge set, and a set $\mathcal{T}$ of triangles in $G$, find a maximum weight $2$-matching containing no…

Data Structures and Algorithms · Computer Science 2019-11-18 Yusuke Kobayashi

Many problems are known to be solvable in subexponential parameterized time when the input graph is planar. The bidimensionality framework of Demaine, Fomin, Hajiaghay, and Thilikos [JACM'05] and the treewidth-pattern-covering approach by…

Data Structures and Algorithms · Computer Science 2026-04-02 Matthias Bentert , Fedor V. Fomin , Petr A. Golovach

We study the \emph{{interval completion}} problem, which asks for the insertion of a set of at most $k$ edges to make a graph of $n$ vertices into an interval graph. We focus on chordal graphs with no small obstructions, where every…

Data Structures and Algorithms · Computer Science 2013-06-14 Yixin Cao

Since its development in the early 90's, parameterized complexity has been widely used to analyze the tractability of many NP-hard combinatorial optimization problems with respect to various types of problem parameters. While the generic…

Data Structures and Algorithms · Computer Science 2017-09-14 Danny Hermelin , Dvir Shabtay , Nimrod Talmon

introduce {\sc Planar Disjoint Paths Completion}, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph $G,$ $k$…

Data Structures and Algorithms · Computer Science 2015-11-18 Isolde Adler , Stavros G. Kolliopoulos , Dimitrios M. Thilikos

A tuple (s1,t1,s2,t2) of vertices in a simple undirected graph is 2-linked when there are two vertex-disjoint paths respectively from s1 to t1 and s2 to t2. A graph is 2-linked when all such tuples are 2-linked. We give a new and simple…

Data Structures and Algorithms · Computer Science 2025-08-15 Samuel Humeau , Damien Pous

Negatively answering a question posed by Mnich and Wiese (Math. Program. 154(1-2):533-562), we show that P2|prec,$p_j{\in}\{1,2\}$|$C_{\max}$, the problem of finding a non-preemptive minimum-makespan schedule for precedence-constrained jobs…

Optimization and Control · Mathematics 2016-05-04 René van Bevern , Robert Bredereck , Laurent Bulteau , Christian Komusiewicz , Nimrod Talmon , Gerhard J. Woeginger

This paper introduces the \emph{$d$-distance $b$-matching problem}, in which we are given a bipartite graph $G=(S,T;E)$ with $S=\{s_1,\dots,s_n\}$, a weight function on the edges, an integer $d\in\mathbb{Z}_+$ and a degree bound function…

Discrete Mathematics · Computer Science 2023-11-29 Péter Madarasi