arXiv subjects

Antonio Lauerbach

Publications and source records attributed to Antonio Lauerbach.

5 recordsLinked to original sources

arXiv2026

Modelling Network Resilience: The Complexity of Some Graph Division Games

Motivated by the controller placement problems in software-defined networks and the fair division principles of classical "cake cutting", we investigate the following two-player zero-sum game. In our model, a defender places a limited number of controllers on graph vertices, while an attacker deletes a limited number of vertices. The defender score is the total number of surviving vertices reachable from any remaining controller. We formalize the computational problems associated with various game dynamics (defender plays first; attacker plays first; players play simultaneously; pure or mixed strategies). We show that these natural problems are $\mathsf{NP}$-complete or $\Sigma^\mathsf{P}_2$-complete, depending on the specific variant. These hardness results provide limitations for optimal controller placement algorithms under different notions of quality of a solution. Finally, we present structural insights that yield efficient algorithms for restricted graph classes (namely interval graphs and graphs of bounded treewidth).

cs.CC↗

arXiv2026

The Parameterized Complexity of Coloring Mixed Graphs

A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring $c$ of a mixed graph $G$ assigns a positive integer to each vertex such that $c(u)\neq c(v)$ for every edge $\{u,v\}$ and $c(u)<c(v)$ for every arc $(u,v)$ of $G$. As in classical coloring, the objective is to minimize the number of colors. Thus, mixed (graph) coloring generalizes classical coloring of undirected graphs and allows for more general applications, such as scheduling with precedence constraints, modeling metabolic pathways, and process management in operating systems; see a survey by Sotskov [Mathematics, 2020]. We initiate the systematic study of the parameterized complexity of mixed coloring. We focus on structural graph parameters that lie between cliquewidth and vertex cover, primarily with respect to the underlying undirected graph. Unlike classical coloring, which is fixed-parameter tractable (FPT) parameterized by treewidth or neighborhood diversity, we show that mixed coloring is W[1]-hard for treewidth and even paraNP-hard for neighborhood diversity. To utilize the directedness of arcs, we introduce and analyze natural generalizations of neighborhood diversity and cliquewidth to mixed graphs, and show that mixed coloring becomes FPT when parameterized by mixed neighborhood diversity. Further, we investigate how these parameters are affected if we add transitive arcs, which do not affect colorings. Finally, we provide tight bounds on the chromatic number of mixed graphs, generalizing known bounds on mixed interval graphs.

cs.CC↗

arXiv2026

Solving the Line-Based Dial-a-Ride Problem by Generating Stopping Patterns

In the line-based dial-a-ride problem (liDARP), vehicles operate along a predefined bus line, with the possibility of skipping stations and turning when empty. Motivated by the practical observation that tight passenger time windows often limit pooling in on-demand services, we introduce a new variant of this transportation system by removing all temporal constraints, which we call the liDARP without TWs. We introduce a new MILP formulation for the liDARP without TWs, which constructs feasible tours as sequences of stopping patterns; first, we consider a fundamental single-vehicle, single-pass special case. Based on our insights, we develop a branch-and-price algorithm where the pricing problem generates profitable stopping patterns. For practical applications, we additionally propose a root node heuristic, using the stopping patterns generated at the root node. Computational experiments show that our branch-and-price algorithm is competitive, finding solutions with a MIP gap of less than 5% for large instances in 60 minutes. Further, the root node heuristic scales to instances with up to 100 requests, outperforming the state-of-the-art and reaching optimality gaps of less than 5% within 15 minutes. This method is highly effective in generating solutions for practical applications, where solving large problems quickly is more valuable than reaching optimality.

math.OC↗

arXiv2025

Eliminating Majority Illusions

An opinion illusion refers to a phenomenon in social networks where agents may witness distributions of opinions among their neighbours that do not accurately reflect the true distribution of opinions in the population as a whole. A specific case of this occurs when there are only two possible choices, such as whether to receive the COVID-19 vaccine or vote on EU membership, which is commonly referred to as a majority illusion. In this work, we study the topological properties of social networks that lead to opinion illusions and focus on minimizing the number of agents that need to be influenced to eliminate these illusions. To do so, we propose an initial, but systematic study of the algorithmic behaviour of this problem. We show that the problem is NP-hard even for underlying topologies that are rather restrictive, being planar and of bounded diameter. We then look for exact algorithms that scale well as the input grows (FPT). We argue the in-existence of such algorithms even when the number of vertices that must be influenced is bounded, or when the social network is arranged in a ``path-like'' fashion (has bounded pathwidth). On the positive side, we present an FPT algorithm for networks with ``star-like'' structure (bounded vertex cover number). Finally, we construct an FPT algorithm for ``tree-like'' networks (bounded treewidth) when the number of vertices that must be influenced is bounded. This algorithm is then used to provide a PTAS for planar graphs.

cs.CC↗

arXiv2024

The Complexity of Counting Turns in the Line-Based Dial-a-Ride Problem

Dial-a-Ride problems have been proposed to model the challenge to consolidate passenger transportation requests with a fleet of shared vehicles. The line-based Dial-a-Ride problem (LiDARP) is a variant where the passengers are transported along a fixed sequence of stops, with the option of taking shortcuts. In this paper we consider the LiDARP with the objective function to maximize the number of transported requests. We investigate the complexity of two optimization problems: the LiDARP, and the problem to determine the minimum number of turns needed in an optimal LiDARP solution, called the MinTurn problem. Based on a number of instance parameters and characteristics, we are able to state the boundary between polynomially solvable and NP-hard instances for both problems. Furthermore, we provide parameterized algorithms that are able to solve both the LiDARP and MinTurn problem.

cs.CC↗