Pascal Kunz
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Efficient parameterized approximation Open
Many problems are NP-hard and, unless P = NP, do not admit polynomial-time exact algorithms. The fastest known exact algorithms exactly usually take time exponential in the input size. Much research effort has gone into obtaining faster ex…
Disentangling the Computational Complexity of Network Untangling Open
We study the network untangling problem introduced by Rozenshtein et al. (Data Min. Knowl. Disc. 35(1), 213–247, 2021), which is a variant of Vertex Cover on temporal graphs–graphs whose edge set changes over discrete time steps. They intr…
In Which Graph Structures Can We Efficiently Find Temporally Disjoint Paths and Walks? Open
A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they d…
Approximate Turing kernelization and lower bounds for domination problems Open
An $α$-approximate polynomial Turing kernelization is a polynomial-time algorithm that computes an $(αc)$-approximate solution for a parameterized optimization problem when given access to an oracle that can compute $c$-approximate solutio…
View article: Parameterized Algorithms for Colored Clustering
Parameterized Algorithms for Colored Clustering Open
In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an en…
View article: On Computing Optimal Tree Ensembles
On Computing Optimal Tree Ensembles Open
Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as …
View article: Parameterized Algorithms for Colored Clustering
Parameterized Algorithms for Colored Clustering Open
In the Colored Clustering problem, one is asked to cluster edge-colored (hyper-)graphs whose colors represent interaction types. More specifically, the goal is to select as many edges as possible without choosing two edges that share an en…
In Which Graph Structures Can We Efficiently Find Temporally Disjoint Paths and Walks? Open
A temporal graph has an edge set that may change over discrete time steps, and a temporal path (or walk) must traverse edges that appear at increasing time steps. Accordingly, two temporal paths (or walks) are temporally disjoint if they d…
Disentangling the Computational Complexity of Network Untangling Open
We study the recently introduced network untangling problem, a variant of Vertex Cover on temporal graphs---graphs whose edge set changes over discrete time steps. There are two versions of this problem. The goal is to select at most k tim…
Disentangling the Computational Complexity of Network Untangling Open
We study the network untangling problem introduced by Rozenshtein, Tatti, and Gionis [DMKD 2021], which is a variant of Vertex Cover on temporal graphs -- graphs whose edge set changes over discrete time steps. They introduce two problem v…
Bipartite Temporal Graphs and the Parameterized Complexity of Multistage 2-Coloring Open
We consider the algorithmic complexity of recognizing bipartite temporal graphs. Rather than defining these graphs solely by their underlying graph or individual layers, we define a bipartite temporal graph as one in which every layer can …
Most Classic Problems Remain NP-Hard on Relative Neighborhood Graphs and Their Relatives Open
Proximity graphs have been studied for several decades, motivated by applications in computational geometry, geography, data mining, and many other fields. However, the computational complexity of classic graph problems on proximity graphs…
Vertex Cover and Feedback Vertex Set Above and Below Structural Guarantees Open
Vertex Cover parameterized by the solution size k is the quintessential fixed-parameter tractable problem. FPT algorithms are most interesting when the parameter is small. Several lower bounds on k are well-known, such as the maximum size …
Most Classic Problems Remain NP-hard on Relative Neighborhood Graphs and\n their Relatives Open
Proximity graphs have been studied for several decades, motivated by\napplications in computational geometry, geography, data mining, and many other\nfields. However, the computational complexity of classic graph problems on\nproximity gra…