Ing. Šimon Schierreich

Stať ve sborníku

10.4230/LIPIcs.MFCS.2024.29

Katedra teoretické informatiky

In the Equitable Connected Partition (ECP for short) problem, we are given a graph $G=(V,E)$ together with an integer $p\in\mathbb{N}$, and our goal is to find a partition of~$V$ into~$p$~parts such that each part induces a connected sub-graph of $G$ and the size of each two parts differs by at most~$1$. On the one hand, the problem is known to be NP-hard in general and W[1]-hard with respect to the path-width, the feedback-vertex set, and the number of parts~$p$ combined. On the other hand, fixed-parameter algorithms are known for parameters the vertex-integrity and the max leaf number. In this work, we systematically study ECP with respect to various structural restrictions of the underlying graph and provide a clear dichotomy of its parameterised complexity. Specifically, we show that the problem is in FPT when parameterized by the modular-width and the distance to clique. Next, we prove W[1]-hardness with respect to the distance to cluster, the $4$-path vertex cover number, the distance to disjoint paths, and the feedback-edge set, and NP-hardness for constant shrub-depth graphs. Our hardness results are complemented by matching algorithmic upper-bounds: we give an XP algorithm for parameterisation by the tree-width and the distance to cluster. We also give an improved FPT algorithm for parameterisation by the vertex integrity and the first explicit FPT algorithm for the $3$-path vertex cover number. The main ingredient of these algorithms is a formulation of ECP as $N$-fold IP, which clearly indicates that such formulations may, in certain scenarios, significantly outperform existing algorithms based on the famous algorithm of Lenstra.

Stať ve sborníku

10.24963/ijcai.2024/296

Katedra teoretické informatiky

We study ways of evaluating the performance of losing projects in participatory budgeting (PB) elections by seeking actions that would have led to their victory. We focus on lowering the projects' costs, obtaining additional approvals for them, and asking supporters to refrain from approving other projects: The larger a change is needed, the less successful is the given project. We seek efficient algorithms for computing our measures and we analyze and compare them experimentally. We focus on the GreedyAV, Phragmen, and Equal-Shares PB rules.

Stať ve sborníku

10.24963/ijcai.2024/308

Katedra teoretické informatiky

In the recently introduced topological distance games, strategic agents need to be assigned to a subset of vertices of a topology. In the assignment, the utility of an agent depends on both the agent's inherent utilities for other agents and its distance from them on the topology. We study the computational complexity of finding individually-rational outcomes; this notion is widely assumed to be the very minimal stability requirement and requires that the utility of every agent in a solution is non-negative. We perform a comprehensive study of the problem's complexity, and we prove that even in very basic cases, deciding whether an individually-rational solution exists is intractable. To reach at least some tractability, one needs to combine multiple restrictions of the input instance, including the number of agents and the topology and the influence of distant agents on the utility.

Stať ve sborníku

10.24963/ijcai.2024/966

Katedra teoretické informatiky

In my research, I focus on computationally hard problems in the area of computational social choice. I am interested in the study of input restrictions that guarantee the existence of efficient and scalable algorithms that are of practical interest.

Článek

10.46298/dmtcs.11591

Katedra teoretické informatiky

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 recent 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.

Stať ve sborníku

10.1609/aaai.v38i9.28822

Katedra teoretické informatiky

We study the computational complexity of fairly allocating a set of indivisible items under externalities. In this recently-proposed setting, in addition to the utility the agent gets from their bundle, they also receive utility from items allocated to other agents. We focus on the extended definitions of envy-freeness up to one item (EF1) and of envy-freeness up to any item (EFX), and we provide the landscape of their complexity for several different scenarios. We prove that it is NP-complete to decide whether there exists an EFX allocation, even when there are only three agents, or even when there are only six different values for the items. We complement these negative results by showing that when both the number of agents and the number of different values for items are bounded by a parameter the problem becomes fixed-parameter tractable. Furthermore, we prove that two-valued and binary-valued instances are equivalent and that EFX and EF1 allocations coincide for this class of instances. Finally, motivated from real-life scenarios, we focus on a class of structured valuation functions, which we term agent/item-correlated. We prove their equivalence to the "standard" setting without externalities. Therefore, all previous results for EF1 and EFX apply immediately for these valuations.

Stať ve sborníku

10.1007/978-981-97-2340-9_19

Katedra teoretické informatiky

Arguably, one of the most central tasks in the area of social network analysis is to identify important members and communities of a given network. The importance of an agent is traditionally measured using some well-defined notion of centrality. In this work, we focus on betweenness centrality, which is based on the number of shortest paths that an agent intersects. This measure can be naturally generalized from a single agent to a group of agents. Specifically, we study the computation complexity of the k-Maximum Betweenness Centrality problem, which consists in finding a group of size $k$ whose betweenness centrality exceeds a given threshold. Since this problem is NP-complete in general, we use the framework of parameterized complexity to reveal at least some tractable fragments. From this perspective, we show that the problem is W[1]-hard and in XP when parameterized by the group size $k$. As the threshold value is not a useful parameter in this context, we focus on the structural restrictions of the underlying social network. In this direction, we show that the problem admits FPT algorithms with respect to the vertex cover number, the distance to clique, or the twin-cover number and the group size combined.

Stať ve sborníku

10.1007/978-3-031-32296-9_5

Katedra teoretické informatiky

We study the following model of disease spread in a social network. In the beginning, 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 neighbours 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 families, such as interval graphs and grid graphs.

Článek

10.1016/j.artint.2023.104017

Katedra teoretické informatiky

Hedonic diversity games are a variant of the classical hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classes (represented as colors in the model) and provided some initial complexity-theoretic and existential results concerning Nash and individually stable outcomes. Here, we design new algorithms accompanied with lower bounds which provide a comprehensive parameterized-complexity picture for computing Nash and individually stable outcomes with respect to the most natural parameterizations of the problem. Crucially, our results hold for general hedonic diversity games where the number of colors is not necessarily restricted to two, and show that---apart from two trivial cases---a necessary condition for tractability in this setting is that the number of colors is bounded by the parameter. Moreover, for the special case of two colors we resolve an open question asked in previous work~(Boehmer and Elkind, AAAI 2020).

Stať ve sborníku

Katedra teoretické informatiky

We propose a novel model for refugee housing respecting the preferences of the accepting community and the refugees themselves. In particular, we are given a topology representing the local community, a set of inhabitants occupying some vertices of topology, and a set of refugees that should be placed on the empty vertices of the graph. Both the inhabitants and the refugees have preferences over the structure of their neighbourhood. We are specifically interested in the problem of finding placements such that the preferences of every individual are met; using game-theoretical words, we are looking for placements that are stable with respect to some well-defined notion of stability. We investigate conditions under which the existence of equilibrium 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 parameterised complexity framework to give a finer-grained view on the problem's complexity with respect to natural parameters and structural restrictions of the given topology.

Stať ve sborníku

10.1609/aaai.v37i13.27018

Katedra teoretické informatiky

Modern social networks are dynamic in their nature; new connections are appearing and old connections are disappearing all the time. However, in our algorithmic and complexity studies, we usually model social networks as static graphs. In this paper, we propose a new paradigm for the study of the well-known Target Set Selection problem, which is a fundamental problem in viral marketing and the spread of opinion through social networks. In particular, we use temporal graphs to capture the dynamic nature of social networks. We show that the temporal interpretation is, unsurprisingly, NP-complete in general. Then, we study computational complexity of this problem for multiple restrictions of both the threshold function and the underlying graph structure and provide multiple hardness lower-bounds.

Stať ve sborníku

10.4204/EPTCS.379.22

Katedra teoretické informatiky

Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function u that took into account distances in a given social network. In this paper, we consider a non-normalized score-based definition of social distance games where the utility function u_v depends on a generic scoring vector v, which may be customized to match the specifics of each individual application scenario. As our main technical contribution, we establish the tractability of computing a welfare-maximizing partitioning of the agents into coalitions on tree-like networks, for every score-based function u_v. We provide more efficient algorithms when dealing with specific choices of u_v or simpler networks, and also extend all of these results to computing coalitions that are Nash stable or individually rational. We view these results as a further strong indication of the usefulness of the proposed score-based utility function: even on very simple networks, the problem of computing a welfare-maximizing partitioning into coalitions remains open for the originally considered canonical function u.

Stať ve sborníku

10.1609/aaai.v37i5.25771

Katedra teoretické informatiky

Microaggregation is a classical statistical disclosure control technique which requires the input data to be partitioned into clusters while adhering to specified size constraints. We provide novel exact algorithms and lower bounds for the task of microaggregating a given network while considering both unrestricted and connected clusterings, and analyze these from the perspective of the parameterized complexity paradigm. Altogether, our results assemble a complete complexity-theoretic picture for the network microaggregation problem with respect to the most natural parameterizations of the problem, including input-specified parameters capturing the size and homogeneity of the clusters as well as the treewidth and vertex cover number of the network.

Stať ve sborníku

Katedra teoretické informatiky

We propose a new discrete model for simultaneously spreading two opinions within a social network inspired by the famous Target Set Selection problem. We are given a social network, a seed-set of agents for each opinion, and two thresholds per agent. The first threshold represents the willingness of an agent to adopt an opinion if she has no opinion at all, while the second threshold states the readiness to acquire a second opinion. The goal is to add as few agents as possible to the initial seed-sets such that, once the process started with these seed-set stabilises, each agent has either both opinions or none. We perform an initial study of its computational complexity. It is not surprising that the problem is NP-hard even in quite restricted settings. Therefore, we investigate the complexity of the problem from the parameterized point-of-view with special focus on sparse networks, which appears often in practice. Among other things, we show that the proposed problem is in the FPT complexity class if we parameterize by the vertex cover number of the underlying graph.

Stať ve sborníku

10.1609/aaai.v36i11.21596

Katedra teoretické informatiky

nformation diffusion in social networks is a well-studied concept in social choice theory. We propose the study of the diffusion of two secrets in a heterogeneous environment from the complexity perspective, that is, there are two different networks with the same set of agents (e.g., the structure of the set of followers might be different in two distinct social networks). Formally, our model combines two group identification processes for which we do have independent desiderata---either constructive, where we would like a given group of agents to be exposed to a secret, or destructive, where a given group of agents should not be exposed to a secret. To be able to reach these targets, we can either delete an agent or introduce a previously latent agent. Our results are mostly negative---all of the problems are NP-hard. Therefore, we propose a parameterized study with respect to the natural parameters, the number of influenced agents, the size of the required/protected agent sets, and the duration of the diffusion process. Most of the studied problems remain W[1]-hard even for a combination of these parameters. We complement these results with nearly optimal XP algorithms.

Stať ve sborníku

Katedra teoretické informatiky

Hedonic diversity games are a variant of the classical Hedonic games designed to better model a variety of questions concerning diversity and fairness. Previous works mainly targeted the case with two diversity classes (represented as colors in the model) and provided a set of initial complexity-theoretic and existential results concerning Nash and Individually stable outcomes. Here, we design new algorithms accompanied with lower bounds which provide a full parameterized-complexity picture for computing Nash and Individually stable outcomes with respect to the most natural parameterizations of the problem. Crucially, our results hold for general Hedonic diversity games where the number of colors is not necessarily restricted to two, and show that---apart from two trivial cases---a necessary condition for tractability in this setting is that the number of colors is bounded by the parameter. Moreover, for the special case of two colors we resolve an open question asked in previous work~(Boehmer and Elkind, AAAI 2020).

Stať ve sborníku

10.4230/LIPIcs.ESA.2022.22

Katedra teoretické informatiky

For many problems, the important instances from practice possess certain structure that one should reflect in the design of specific algorithms. As data reduction is an important and inextricable part of today’s computation, we employ one of the most successful models of such precomputation - the kernelization. Within this framework, we focus on Traveling Salesperson Problem (TSP) and some of its generalizations. We provide a kernel for TSP with size polynomial in either the feedback edge set number or the size of a modulator to constant-sized components. For its generalizations, we also consider other structural parameters such as the vertex cover number and the size of a modulator to constant-sized paths. We complement our results from the negative side by showing that the existence of a polynomial-sized kernel with respect to the fractioning number, the combined parameter maximum degree and treewidth, and, in the case of {Subset TSP}, modulator to disjoint cycles (i.e., the treewidth two graphs) is unlikely.

Článek

10.1016/j.ipl.2021.106165

Katedra teoretické informatiky

In the Waypoint Routing Problem one is given an undirected capacitated and weighted graph G, a source-destination pair s, t∈V(G) and a set W⊆V(G), of waypoints. The task is to find a walk which starts at the source vertex s, visits, in any order, all waypoints, ends at the destination vertex t, respects edge capacities, that is, traverses each edge at most as many times as is its capacity, and minimizes the cost computed as the sum of costs of traversed edges with multiplicities. We study the problem for graphs of bounded treewidth and present a new algorithm for the problem working in 2^{O(tw)}·n time, significantly improving upon the previously known algorithms. We also show that this running time is optimal for the problem under Exponential Time Hypothesis