arXiv subjects

Tom-Lukas Breitkopf

Publications and source records attributed to Tom-Lukas Breitkopf.

7 recordsLinked to original sources

arXiv2026

Parameterized Complexity of Temporal Agony

Real-world networks are often organized in several layers forming a hierarchy which determines the interaction between the individual components. In order to discover such hierarchies in temporal networks, Tatti [ECML PKDD 2018] introduced the temporal agony problem Seg-Agony. Here, the goal is to assign each vertex a certain rank (from 1 to $k$) such that arcs only point from lower ranks to higher ranks. Backward arcs are penalized depending on the difference between the corresponding ranks. Since arcs may change over time, each vertex is allowed to change its rank $\ell\ge 1$ times in order to minimize the overall penalty $α$ (called temporal agony). We study the parameterized complexity of Seg-Agony with a special focus on the number $k$ of possible ranks for which we identify the precise complexity border. We show that the problem is polynomial-time solvable for $k=2$, NP-hard for $k=3$ and $\ell=1$ but polynomial-time solvable for constant $α$, and NP-hard for $k=4$ and $\ell=1$ even for $α=0$. We further show a polynomial-time algorithm for a constant number $n$ of vertices and fixed-parameter tractability for the combined parameter $n+\ell$.

cs.DS↗

arXiv2026

On the Parameterized Complexity of Bounded-Density Vertex Deletion

We explore the parameterized complexity of Bounded Density Vertex Deletion (BDVD): given a graph $G$, an integer budget $k$, and a target density $τ_ρ$, the task is to determine whether the density (i.e. number of edges divided by number of vertices) of the densest subgraph of $G$ can be reduced to at most $τ_ρ$ by deleting at most $k$ vertices. Our primary focus is on structural graph parameters related to treewidth, as the parameterized complexity of BDVD with respect to treewidth was left as open question by Bazgan et al. [JCSS, 2025]. We resolve this question by showing W[1]-hardness with respect to various parameters, including treedepth and feedback vertex number. These results imply W[1]-hardness with respect to treewidth. We obtain positive results for parameters larger than treedepth and feedback vertex number, namely we show BDVD is in FPT parameterized by the max leaf number or vertex integrity. Under the assumption that the target density $τ_ρ$ is a fixed constant the parameterized complexity landscape of BDVD changes drastically, allowing a fixed-parameter tractable algorithm even for parameters smaller than treewidth, namely cliquewidth. Altogether, our results provide a refined complexity landscape for Bounded Density Vertex Deletion, sharply distinguishing between tractable and intractable parameter regimes under structural parameterizations.

cs.DS↗

arXiv2026

Ranking Opinions with Few States in Population Protocols

Population protocols are a model of distributed computing where $n$ agents, each a simple finite-state machine, interact in pairs to solve a common task against a (adversarial) interaction scheduler. This model was intensively studied in recent years; in particular, the problem of relative majority received much attention: Each agent starts with an input opinion (or color) out of $k$ possibilities, and the goal is for each agent to eventually output the color with the largest support in the population. Before our work, the state complexity (the minimum number of states required per agent) was only known to be between $Ω(k^2)$ and $O(k^{7})$. Our main contribution is a population protocol that solves the relative majority problem with $k^3$ states. We achieve this result with a new protocol called CIRCLES. While prior approaches in the literature relied on duels of agents to find the majority color -- an approach that proved effective for the case with two colors -- CIRCLES partitions the agents into circular linked lists of decreasing sizes, with the property that no two agents with the same initial color lie in the same circle. We show that CIRCLES always correctly computes the desired structure against the most adversarial of schedulers (weakly fair). We then show that a trivial extension of CIRCLES solves the relative majority problem. We extend our protocol to handle various tie-breaking mechanisms or to support the case where the agents do not share a prior ordering of the colors. Finally, we show that a modification of CIRCLES solves the ranking problem with $2 \cdot k^4$ states, where each agent must output the rank of its initial color in the population.

cs.DC↗

arXiv2026

Parameterized Algorithms for Computing MAD Trees

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 and polynomial-time algorithms for some graph classes are known, the parameterized complexity of the problem has not been investigated so far. We start a parameterized complexity analysis with the goal of determining the border of algorithmic tractability for the MAD tree problem. To this end, we provide a linear-time algorithm for graphs of constant modular width and a polynomial-time algorithm for graphs of bounded treewidth; the degree of the polynomial depends on the treewidth. That is, the problem is in FPT with respect to modular width and in XP with respect to treewidth. Moreover, we show it is in FPT when parameterized by vertex integrity or by an above-guarantee parameter. We complement these algorithms with NP-hardness on split graphs.

cs.DS↗

arXiv2026

Density Matters: A Complexity Dichotomy of Deleting Edges to Bound Subgraph Density

We study $τ$-Bounded-Density Edge Deletion ($τ$-BDED), where given an undirected graph $G$, the task is to remove as few edges as possible to obtain a graph $G'$ where no subgraph of $G'$ has density more than $τ$. The density of a (sub)graph is the number of edges divided by the number of vertices. This problem was recently introduced and shown to be NP-hard for $τ\in \{2/3, 3/4, 1 + 1/25\}$, but polynomial-time solvable for $τ\in \{0,1/2,1\}$ [Bazgan et al., JCSS 2025]. We provide a complete dichotomy with respect to the target density $τ$: 1. If $2τ\in \mathbb{N}$ (half-integral target density) or $τ< 2/3$, then $τ$-BDED is polynomial-time solvable. 2. Otherwise, $τ$-BDED is NP-hard. We complement the NP-hardness with fixed-parameter tractability with respect to the treewidth of $G$. Moreover, for integral target density $τ\in \mathbb{N}$, we show $τ$-BDED to be solvable in randomized $O(m^{1 + o(1)})$ time. Our algorithmic results are based on a reduction to a new general flow problem on restricted networks that, depending on $τ$, can be solved via Maximum s-t-Flow or General Factors. We believe this connection between these variants of flow and matching to be of independent interest.

cs.DS↗

arXiv2025

Brief Announcement: Minimizing Energy Solves Relative Majority with a Cubic Number of States in Population Protocols

This paper revisits a fundamental distributed computing problem in the population protocol model. Provided $n$ agents each starting with an input color in $[k]$, the relative majority problem asks to find the predominant color. In the population protocol model, at each time step, a scheduler selects two agents that first learn each other's states and then update their states based on what they learned. We present the \textsc{Circles} protocol that solves the relative majority problem with $k^3$ states. It is always-correct under weakly fair scheduling. Not only does it improve upon the best known upper bound of $O(k^7)$, but it also shows a strikingly simpler design inspired by energy minimization in chemical settings.

cs.DC↗

arXiv2022

Advanced Deep Learning Architectures for Accurate Detection of Subsurface Tile Drainage Pipes from Remote Sensing Images

Subsurface tile drainage pipes provide agronomic, economic and environmental benefits. By lowering the water table of wet soils, they improve the aeration of plant roots and ultimately increase the productivity of farmland. They do however also provide an entryway of agrochemicals into subsurface water bodies and increase nutrition loss in soils. For maintenance and infrastructural development, accurate maps of tile drainage pipe locations and drained agricultural land are needed. However, these maps are often outdated or not present. Different remote sensing (RS) image processing techniques have been applied over the years with varying degrees of success to overcome these restrictions. Recent developments in deep learning (DL) techniques improve upon the conventional techniques with machine learning segmentation models. In this study, we introduce two DL-based models: i) improved U-Net architecture; and ii) Visual Transformer-based encoder-decoder in the framework of tile drainage pipe detection. Experimental results confirm the effectiveness of both models in terms of detection accuracy when compared to a basic U-Net architecture. Our code and models are publicly available at https://git.tu-berlin.de/rsim/drainage-pipes-detection.

cs.CV↗