arXiv subjects

Dušan Knop

Publications and source records attributed to Dušan Knop.

At least 19 recordsLinked to original sources

arXiv2026

Practical approach to $2$-Euclidean Preferences

An election is a pair $(C,V)$ of candidates and voters. Each vote is a ranking (permutation) of the candidates. An election is $d$-Euclidean if there is an embedding of both candidates and voters into $\mathbb{R}^d$ such that voter $v$ prefers candidate $a$ over $b$ if and only if $a$ is closer to $v$ than $b$ is to $v$ in the embedding. For $d\geq 2$ the problem of deciding whether $(C,V)$ is $d$-Euclidean is $\exists \mathbb{R}$-complete. In this paper, we propose a practical approach to recognizing and refuting $2$-Euclidean preferences. We design a new class of forbidden substructures that works very well on practical instances. We utilize the framework of integer linear programming (ILP) and quadratically constrained programming (QCP). We also introduce reduction rules that simplify many real-world instances significantly. Our approach beats the previous algorithm of Escoffier, Spanjaard and Tydrichová~[Algorithmic Recognition of 2-Euclidean Preferences, ECAI 2023] both in number of resolved instances and the running time. In particular, we were able to lower the number of unresolved PrefLib instances from $343$ to $60$. Moreover, $98.7\%$ of PrefLib instances are resolved in under $1$ second using our approach.

cs.GT↗

arXiv2026

Exact Algorithms for Distance to Unique Vertex Cover

Horiyama et al. (AAAI 2024) studied the problem of generating graph instances that possess a unique minimum vertex cover under specific conditions. Their approach involved pre-assigning certain vertices to be part of the solution or excluding them from it. Notably, for the \textsc{Vertex Cover} problem, pre-assigning a vertex is equivalent to removing it from the graph. Horiyama et al.~focused on maintaining the size of the minimum vertex cover after these modifications. In this work, we extend their study by relaxing this constraint: our goal is to ensure a unique minimum vertex cover, even if the removal of a vertex may not incur a decrease on the size of said cover. Surprisingly, our relaxation introduces significant theoretical challenges. We observe that the problem is $Σ^2_P$-complete, and remains so even for planar graphs of maximum degree 5. Nevertheless, we provide a linear time algorithm for trees, which is then further leveraged to show that MU-VC is in \textsf{FPT} when parameterized by the combination of treewidth and maximum degree. Finally, we show that MU-VC is in \textsf{XP} when parameterized by clique-width while it is fixed-parameter tractable (FPT) if we add the size of the solution as part of the parameter.

cs.DS↗

arXiv2026

Core stability recognition for minimum-cost spanning tree games: Parameterized perspective

Minimum-cost spanning tree game (MSTG) is a cooperative game played on an undirected edge-weighted graph $(G,w)$ representing the network, where each vertex corresponds to a player and each edge has an associated cost~$w$. A distinguished vertex $s \in V(G)$ represents the supply or source. For any coalition of players $S$, the characteristic cost function $c(S)$ is defined as the minimum cost of a spanning tree with respect to $w$, connecting exactly the vertices in $S \cup \{s\}$. In this paper we study the computational complexity of deciding core membership for MSTG. In general, deciding whether a given allocation is in the core is \textsf{coNP}-hard~(Faigle et al.,International Journal of Game Theory,1997). We study the core recognition problem under the name {\sc MSTG Core Non-Membership}. We extend the hardness to graphs which are very close to being planar. On the positive side, we present several algorithmic results within the framework of parameterized complexity. We show that {\sc MSTG Core Non-Membership} is fixed-parameter tractable when parameterized by the support size of the allocation. Turning into structural parameters of graphs, we show that the problem admits an FPT algorithm parameterized by treewidth and signed neighborhood diversity. Last but not least, we investigate kernelization. While in general graphs, under standard complexity-theoretical assumptions, {\sc MSTG Core Non-Membership} does not admit a polynomial kernel parameterized by the vertex cover number, we design a cubic kernel in planar graphs. Furthermore, in general graphs, we obtain quadratic kernel for signed neighborhood diversity and linear kernel for the parameter feedback edge number.

cs.GT↗

arXiv2026

Parameterized Complexity of Scheduling Problems in Robotic Process Automation

This paper studies the growing domain of Robotic Process Automation (RPA) problems. Motivated by scheduling problems arising in RPA, we study the parameterized complexity of the single-machine problem with precedence constraints, release times, and deadlines (i.e., the problem known as $1|\operatorname{prec},r_j,d_j|*$ in the three-field notation). We focus on parameters naturally linked to RPA systems, including chain-like precedences, the number of distinct processing times, and the structure of the time windows. We show that the problem is strongly XNLP-hard parameterized by the number of chains, even with only two prescribed processing times and two distinct time-window lengths. The problem remains XNLP-hard even under prec-consistent time windows. On the positive side, we obtain polynomial-time algorithm when all jobs share a single time-window length and FPT when the processing times, release times and deadlines are chain-uniform. We also show that the problem lies in XNLP when parameterized by the width of the precedence relation either when the instance is encoded in unary or the processing times are bounded.

cs.DS↗

arXiv2026

Parameterized Complexity of Connected Network Microaggregation: The Role of Cluster Size

Network microaggregation is a fundamental technique in statistical disclosure control, where vertices of a graph are partitioned into clusters satisfying size constraints and admitting a center within bounded distance. We study the parameterized complexity of the \emph{unweighted Connected Network Microaggregation} problem, focusing on structural parameters and natural clustering parameters such as the distance bound $d$ and cluster size gap $u-\ell$. We show that, unlike the weighted variant, the unweighted connected problem is fixed-parameter tractable when parameterized by neighborhood diversity, and hence by vertex cover. In contrast, it remains $\mathrm{W[1]}$-hard for more general structural parameters, including vertex deletion to paths, stars, and cliques. These hardness results hold even for every $d\ge 2$ and any fixed gap $u-\ell$, showing that these clustering parameters do not overcome the structural hardness. We further show that adding the cluster size bound $u$ restores tractability for structural parameters such as treewidth and cluster vertex deletion. Moreover, $u$ is essential: the problem remains $\mathrm{W[1]}$-hard when these structural parameters are considered alone. For kernelization, we prove that the problem has no polynomial kernel parameterized by vertex cover unless $\mathrm{coNP}\subseteq\mathrm{NP/poly}$, even when the distance constraint is vacuous. Adding $u$ yields a polynomial kernel for vertex cover, while kernelization remains unlikely for more general structural parameters even when combined with $u$. Finally, we show that the problem is NP-hard on graphs of bounded clique-width.

cs.DS↗

arXiv2026

Balancing the Spread of Two Opinions in Sparse Social Networks

Inspired by the famous Target Set Selection problem, we propose a new discrete model to simultaneously spread two opinions within a social network and perform an initial study of its complexity. Here, we are given a social network, a seed-set of agents for each opinion, two thresholds for each agent, a budget, and a number of rounds. The first threshold represents the willingness of an agent to adopt an opinion if the agent has no opinion at all, while the second threshold states the willingness to acquire a second opinion if the agent already has one. The goal is to add at most budget-many agents to the initial seed-sets such that the process started with these extended seed-sets stabilizes within the given number of rounds, with each agent having either both opinions or none. That is, our goal is to ensure that the spread of opinions is balanced. We show that the problem is NP-hard, and thus we study the problem from the perspective of parameterized complexity. In particular, we show that the problem is FPT when parameterized by the number of rounds, the maximum threshold, and the treewidth combined. This algorithm also applies to the combined parameter, the treedepth and the maximum threshold. Finally, we show that the problem is FPT when parameterized by the vertex cover number, the $3$-path vertex cover number, or the vertex integrity of the input network alone. To complement our tractability results, we show that the problem is W[1]-hard with respect to a) the sizes of the initial seed-sets and the feedback-vertex set number combined, even if all thresholds are bounded by a constant, and b) the budget, the 4-path vertex cover number, and the feedback-vertex set number combined, even if every activation process stabilizes in at most 4 rounds.

cs.DS↗

arXiv2026

Stability in Distance Preservation Games on Graphs

We introduce a new class of network allocation games called graphical distance preservation games. Here, we are given a graph, called a topology, and a set of agents that need to be allocated to its vertices. Moreover, every agent has an ideal (and possibly different) distance in which to be from some of the other agents. Given an allocation of agents, each one of them suffers a cost that is the sum of the differences from the ideal distance for each agent in their subset. The goal is to decide whether there is a stable allocation of the agents, i.e., no agent would like to deviate from their location. Specifically, we consider three different stability notions: envy-freeness, swap stability, and jump stability. We perform a comprehensive study of the (parameterized) complexity of the problem in three different dimensions: the topology of the graph, the number of agents, and the structure of preferences of the agents.

cs.GT↗

arXiv2026

Parameterized Critical Node Cut Revisited

We study how to sparsify connectivity in graphs under a tight deletion budget. Given a graph $G$ and integers $k,x \ge 0$, Critical Node Cut (CNC) asks whether we can delete at most $k$ vertices so that the number of remaining unordered pairs of connected vertices is at most $x$. CNC generalizes Vertex Cover (the case $x=0$) and models tasks in network design, epidemiology, and social network analysis. We comprehensively map the structural parameterized complexity landscape for Critical Node Cut. First, we prove W[1]-hardness for the combined parameter $k + \mathrm{fes} + Δ+ \mathrm{pw}$, where $\mathrm{fes}$ is the feedback edge set number, $Δ$ the maximum degree, and $\mathrm{pw}$ the pathwidth of the input graph respectively. This significantly improves over the known W[1]-hardness for $k+\mathrm{tw}$, where $\mathrm{tw}$ denotes the treewidth, and is tight in that tree-depth together with maximum degree trivially yields FPT. Second, we give new positive results. Specifically, we identify three structural parameters--max-leaf number, vertex integrity, and modular-width--that render the problem fixed-parameter tractable, and develop a polynomial-time algorithm for graphs of constant clique-width. Third, leveraging a technique introduced by Lampis~[ICALP '14], we develop an FPT approximation scheme that, for any $\varepsilon > 0$, computes a $(1+\varepsilon)$-approximate solution in time $(\mathrm{tw} / \varepsilon)^{\mathcal{O}(\mathrm{tw})} n^{\mathcal{O}(1)}$, where $\mathrm{tw}$ denotes the treewidth of the input graph. Finally, we show that CNC admits no polynomial kernel when parameterized by vertex cover number, unless standard assumptions fail. Together, these results substantially sharpen the known complexity landscape for CNC.

cs.DS↗

arXiv2026

Participatory Budgeting Project Strength via Candidate Control

We study the complexity of candidate control in participatory budgeting elections. The goal of constructive candidate control is to ensure that a given candidate wins by either adding or deleting candidates from the election (in the destructive setting, the goal is to prevent a given candidate from winning). We show that such control problems are NP-hard to solve for many participatory budgeting voting rules, including Phragmén and Method of Equal Shares, but there are natural cases with polynomial-time algorithms (e.g., for the GreedyAV rule and projects with costs encoded in unary). We also argue that control by deleting candidates is a useful tool for assessing the performance (or, strength) of initially losing projects, and we support this view with experiments.

cs.GT↗

arXiv2025

Dividing Indivisible Items for the Benefit of All: It is Hard to Be Fair Without Social Awareness

In standard fair division models, we assume that all agents are selfish. However, in many scenarios, division of resources has a direct impact on the whole group or even society. Therefore, we study fair allocations of indivisible items that, at the same time, maximize social impact. In this model, each agent is associated with two additive functions that define their value and social impact for each item. The goal is to allocate items so that the social impact is maximized while maintaining some fairness criterion. We reveal that the complexity of the problem heavily depends on whether the agents are socially aware, i.e., they take into consideration the social impact functions. For socially unaware agents, we prove that the problem is NP-hard for a variety of fairness notions, and that it is tractable only for very restricted cases, e.g., if, for every agent, the valuation equals social impact and it is binary. On the other hand, social awareness allows for fair allocations that maximize social impact, and such allocations can be computed in polynomial time. Interestingly, the problem becomes again intractable as soon as the definition of social awareness is relaxed.

cs.GT↗

arXiv2025

Pathfinding in Self-Deleting Graphs

In this paper, we study the problem of pathfinding on traversal-dependent graphs, i.e., graphs whose edges change depending on the previously visited vertices. In particular, we study \emph{self-deleting graphs}, introduced by Carmesin et al. (Sarah Carmesin, David Woller, David Parker, Miroslav Kulich, and Masoumeh Mansouri. The Hamiltonian cycle and travelling salesperson problems with traversal-dependent edge deletion. J. Comput. Sci.), which consist of a graph $G=(V, E)$ and a function $f\colon V\rightarrow 2^E$, where $f(v)$ is the set of edges that will be deleted after visiting the vertex $v$. In the \textsc{(Shortest) Self-Deleting $s$-$t$-path} problem we are given a self-deleting graph and its vertices $s$ and $t$, and we are asked to find a (shortest) path from $s$ to $t$, such that it does not traverse an edge in $f(v)$ after visiting $v$ for any vertex $v$. We prove that \textsc{Self-Deleting $s$-$t$-path} is NP-hard even if the given graph is outerplanar, bipartite, has maximum degree $3$, bandwidth $2$ and $|f(v)|\leq 1$ for each vertex $v$. We show that \textsc{Shortest Self-Deleting $s$-$t$-path} is W[1]-complete parameterized by the length of the sought path and that \textsc{Self-Deleting $s$-$t$-path} is \W{1}-complete parameterized by the vertex cover number, feedback vertex set number and treedepth. We also show that the problem becomes FPT when we parameterize by the maximum size of $f(v)$ and several structural parameters. Lastly, we show that the problem does not admit a polynomial kernel even for parameterization by the vertex cover number and the maximum size of $f(v)$ combined already on 2-outerplanar graphs.

cs.DS↗

arXiv2025

Density of Traceable Graphs

We establish tight lower and upper bounds on the number of edges in traceable graphs in several classes of dense graphs. A graph is traceable if it has a Hamiltonian path. We show that the bound is: - quadratic for the class of graphs of bounded neighborhood diversity, bounded size of maximum induced matching or bounded cluster vertex deletion number; - n log n for the class of cographs or, more generaly, bounded modular-width, and for the class of bounded distance to cograph; and - sligthly superlinear for the class of bounded shrub-depth.

math.CO↗

arXiv2025

When Agents Break Down in Multiagent Path Finding

In Multiagent Path Finding (MAPF), the goal is to compute efficient, collision-free paths for multiple agents navigating a network from their sources to targets, minimizing the schedule's makespan-the total time until all agents reach their destinations. We introduce a new variant that formally models scenarios where some agents may experience delays due to malfunctions, posing significant challenges for maintaining optimal schedules. Recomputing an entirely new schedule from scratch after each malfunction is often computationally infeasible. To address this, we propose a framework for dynamic schedule adaptation that does not rely on full replanning. Instead, we develop protocols enabling agents to locally coordinate and adjust their paths on the fly. We prove that following our primary communication protocol, the increase in makespan after k malfunctions is bounded by k additional turns, effectively limiting the impact of malfunctions on overall efficiency. Moreover, recognizing that agents may have limited computational capabilities, we also present a secondary protocol that shifts the necessary computations onto the network's nodes, ensuring robustness without requiring enhanced agent processing power. Our results demonstrate that these protocols provide a practical, scalable approach to resilient multiagent navigation in the face of agent failures.

cs.MA↗

arXiv2025

Solving Multiagent Path Finding on Highly Centralized Networks

The Mutliagent Path Finding (MAPF) problem consists of identifying the trajectories that a set of agents should follow inside a given network in order to reach their desired destinations as soon as possible, but without colliding with each other. We aim to minimize the maximum time any agent takes to reach their goal, ensuring optimal path length. In this work, we complement a recent thread of results that aim to systematically study the algorithmic behavior of this problem, through the parameterized complexity point of view. First, we show that MAPF is NP-hard when the given network has a star-like topology (bounded vertex cover number) or is a tree with $11$ leaves. Both of these results fill important gaps in our understanding of the tractability of this problem that were left untreated in the recent work of [Fioravantes et al. Exact Algorithms and Lowerbounds for Multiagent Path Finding: Power of Treelike Topology. AAAI'24]. Nevertheless, our main contribution is an exact algorithm that scales well as the input grows (FPT) when the topology of the given network is highly centralized (bounded distance to clique). This parameter is significant as it mirrors real-world networks. In such environments, a bunch of central hubs (e.g., processing areas) are connected to only few peripheral nodes.

cs.CC↗

arXiv2025

Exact Algorithms for Multiagent Path Finding with Communication Constraints on Tree-Like Structures

Consider the scenario where multiple agents have to move in an optimal way through a network, each one towards their ending position while avoiding collisions. By optimal, we mean as fast as possible, which is evaluated by a measure known as the makespan of the proposed solution. This is the setting studied in the Multiagent Path Finding problem. In this work, we additionally provide the agents with a way to communicate with each other. Due to size constraints, it is reasonable to assume that the range of communication of each agent will be limited. What should be the trajectories of the agents to, additionally, maintain a backbone of communication? In this work, we study the Multiagent Path Finding with Communication Constraint problem under the parameterized complexity framework. Our main contribution is three exact algorithms that are efficient when considering particular structures for the input network. We provide such algorithms for the case when the communication range and the number of agents (the makespan resp.) are provided in the input and the network has a tree topology, or bounded maximum degree (has a tree-like topology, i.e., bounded treewidth resp.). We complement these results by showing that it is highly unlikely to construct efficient algorithms when considering the number of agents as part of the input, even if the makespan is $3$ and the communication range is $1$.

cs.CC↗

arXiv2025

Host Community Respecting Refugee Housing

We propose a novel model for refugee housing respecting the preferences of the accepting community and refugees themselves. In particular, we are given a topology representing the local community, a set of inhabitants occupying some vertices of the topology, and a set of refugees that should be housed on the empty vertices of the graph. Both the inhabitants and the refugees have preferences over the structure of their neighborhood. We are specifically interested in the problem of finding housing such that the preferences of every individual are met; using game-theoretical words, we are looking for housing that is stable with respect to some well-defined notion of stability. We investigate conditions under which the existence of equilibria is guaranteed and study the computational complexity of finding such a stable outcome. As the problem is NP-hard even in very simple settings, we employ the parameterized complexity framework to give a finer-grained view of the problem's complexity with respect to natural parameters and structural restrictions of the given topology.

cs.GT↗

arXiv2025

Balanced and Fair Partitioning of Friends

In the recently introduced model of fair partitioning of friends, there is a set of agents located on the vertices of an underlying graph that indicates the friendships between the agents. The task is to partition the graph into $k$ balanced-sized groups, keeping in mind that the value of an agent for a group equals the number of edges they have in that group. The goal is to construct partitions that are "fair", i.e., no agent would like to replace an agent in a different group. We generalize the standard model by considering utilities for the agents that are beyond binary and additive. Having this as our foundation, our contribution is threefold (a) we adapt several fairness notions that have been developed in the fair division literature to our setting; (b) we give several existence guarantees supported by polynomial-time algorithms; (c) we initiate the study of the computational (and parameterized) complexity of the model and provide an almost complete landscape of the (in)tractability frontier for our fairness concepts.

cs.GT↗

arXiv2024

On the Complexity of Target Set Selection in Simple Geometric Networks

We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a healthy individual gets infected if and only if a sufficient number of its direct neighbors are already infected. We represent the social network as a graph. Inspired by the real-world restrictions in the current epidemic, especially by social and physical distancing requirements, we restrict ourselves to networks that can be represented as geometric intersection graphs. We show that finding a minimal vertex set of initially infected individuals to spread the disease in the whole network is computationally hard, already on unit disk graphs. Hence, to provide some algorithmic results, we focus ourselves on simpler geometric graph classes, such as interval graphs and grid graphs.

cs.CC↗