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Lutz Oettershagen

Publications and source records attributed to Lutz Oettershagen.

At least 19 recordsLinked to original sources
arXiv2026

Fair Top-k Katz Centrality via Graph Design

Centrality measures are widely used to rank nodes in networked data, but fairness interventions for graph centrality typically target global score mass or modify the centrality operator rather than controlling who appears in the displayed top-k ranking. We study this top-k setting for Katz centrality. Given a target group proportion, an admissible set of directed edge additions, and a fairness tolerance, the goal is to find the smallest edit set whose resulting Katz top-k ranking satisfies the target representation constraint. We formalize this problem as Fair Top-k Katz Centrality Design and show that the minimum-edit objective is strongly inapproximable, ruling out worst-case polynomial-time approximation guarantees unless P = NP. We then derive closed-form Katz sensitivity expressions showing that useful edits are boundary-driven: they must help promotable nodes outside the top-k set overtake opposing nodes inside it. Based on this structure, we develop BLADE, a scalable boundary-link algorithm that avoids dense Katz-kernel maintenance by using score-based direct-target batches and warm-started Katz updates. Experiments on synthetic and real-world networks show that BLADE reaches the desired top-k representation using far fewer edits than natural baselines, while scaling to large real-world graphs and preserving the original ranking structure.

cs.SI↗
arXiv2026

Fair Minimum Labeling: Efficient Temporal Network Activations for Reachability and Equity

Balancing resource efficiency and fairness is critical in networked systems that support modern learning applications. We introduce the \emph{Fair Minimum Labeling} (FML) problem: the task of designing a minimum-cost temporal edge activation plan that ensures each group of nodes in a network has sufficient access to a designated target set, according to specified coverage requirements. FML captures key trade-offs in systems where edge activations incur resource costs and equitable access is essential, such as distributed data collection, update dissemination in edge-cloud systems, and fair service restoration in critical infrastructure. We first give a structural characterisation of the single-terminal case, showing that it is equivalent to the rooted Covering Steiner problem. We prove that FML is NP-hard and admits no $((1-ε)\ln |\mathcal{C}|)$-approximation for $|\mathcal{C}|$ groups, already on a star, while for any fixed number of groups it inherits a constant-factor approximation and remains APX-hard. We then present probabilistic approximation algorithms for the two-group, single-terminal case: an algorithm whose tree subroutine is exact, hence optimal on tree-structured networks and $\mathcal{O}(\log |V|)$ in expectation on general graphs, together with a faster bicriteria variant whose coverage violation degrades gracefully with the merge depth of the tree computation. For practical scalability, we additionally introduce a graph-native variant based on a shortest-path-tree reduction. Empirical results show that FML enforces group-level fairness, while the graph-native variant substantially improves scalability and achieves competitive activation cost.

cs.SI↗
arXiv2026

Unsupervised Multi-Scale Gromov-Wasserstein Hypergraph Alignment

We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information, without node features, labels, seed matches, or side information. Direct higher-order formulations can represent hyperedge interactions faithfully, but they can be computationally demanding and cumbersome for non-uniform hypergraphs. Graph-reduction approaches introduce a different challenge: clique expansions keep the alignment problem on the original node set but collapse all hyperedge evidence into one pairwise graph, whereas bipartite expansions preserve incidence structure but enlarge the problem from nodes to nodes plus hyperedges. We introduce FALCON (Filtration-based hypergrAph aLignment via Cross-scale Optimal traNsport), an unsupervised optimal-transport framework for hypergraph alignment. Instead of representing each hypergraph by a single collapsed clique graph, FALCON constructs a filtration-induced sequence of clique-based co-occurrence dissimilarity matrices and jointly aligns all levels through one shared multi-scale Gromov--Wasserstein (GW) objective. The shared transport plan enforces a globally consistent node correspondence across filtration levels while avoiding the auxiliary hyperedge nodes introduced by bipartite expansion. Experiments on perturbation benchmarks derived from real-world hypergraphs show that FALCON is robust to structural noise and in almost all cases outperforms strong graph- and hypergraph-alignment baselines.

cs.LG↗
arXiv2026

Linguistic Monoculture in LLM-Assisted Language Use

Writing and communication are increasingly mediated by large language models (LLMs) that are being used to draft, revise and polish text. Although such assistance can improve clarity and help authors meet institutional expectations, widespread reliance on shared models may reduce population-level variation in linguistic form, a phenomenon we refer to as linguistic monoculture. We develop a mathematical framework in which authors and LLMs are represented as distributions over linguistic features and coevolve through repeated interaction. We analyze three interaction mechanisms: a shared model with a fixed linguistic distribution, a shared model recursively updated from author outputs, and personalized models updated through author-specific and population-level feedback. We characterize the resulting equilibria and convergence rates, showing that, shared models can drive authors toward a common norm, recursive feedback relocates the shared norm without altering pairwise spread under common conformity, and personalization can preserve a family of distinct author-model equilibria with nonzero linguistic diversity. We then endogenize conformity as a strategic choice trading off private benefits from clarity, legibility, and perceived fluency against distinctive style. Within this utility model, individually rational authors may conform more than is socially optimal because they do not internalize the value their distinctiveness provides to others, creating a negative externality and a price of monoculture that is finite for each fixed instance but can grow without bound when distinctiveness dominates authenticity. Synthetic simulations illustrate how fixed shared assistance, recursive feedback, and personalization produce different long-run diversity outcomes.

cs.AI↗
arXiv2026

Query-Limited Community Recovery in Stochastic Block Models

We study exact community recovery in the two-community stochastic block model on $n$ vertices under limited and noisy access to network data. The learner may query a noisy neighborhood oracle that reveals each true neighbor of a queried vertex independently with fixed probability and never returns non-neighbors, subject to a finite query budget. We consider both oracle-only access and a combined model where the learner also observes a single subsampled copy of the underlying graph. For oracle-only access, balanced uniform querying gives a sharp non-adaptive benchmark: when each vertex is queried the same integer number of times, the observations reduce to an SBM with attenuated edge probabilities and the Abbe-Bandeira-Hall exact-recovery threshold applies. We show that this benchmark is not adaptively optimal: a two-stage adaptive strategy succeeds with $n+o(n)$ queries in a regime where balanced uniform querying requires $m n$ queries for some $m>1$. With an additional subsampled graph, we prove a sublinear-query adaptivity gap: balanced data-independent uniform querying with a sublinear budget does not improve over the subsampled graph alone, whereas adaptive querying can target a small set of uncertain vertices and achieve exact recovery. Thus adaptive data acquisition can strictly improve the information-theoretic limits of exact recovery.

cs.IT↗
arXiv2026

A Hierarchical Quantized Tokenization Framework for Task-Adaptive Graph Representation Learning

Foundation models in language and vision benefit from a unified discrete token interface that converts raw inputs into sequences for scalable pre-training and inference. For graphs, an effective tokenizer should yield reusable discrete codes that capture both node semantics and relational structure across scales, yet prior quantization-based graph tokenizers typically combine residual vector quantization (RVQ) levels with fixed rules and often focus on a single structural view, limiting cross-task transfer. We present a hierarchical quantized tokenization framework with task-conditioned routing and dual-view token streams. It produces multi-scale codes and two synchronized sequences: a local stream that preserves node-level information and a diffusion-style multi-hop stream that summarizes connectivity. A lightweight router learns task-dependent mixtures over RVQ depths to select an appropriate granularity, while a gated cross-attention module aligns and fuses the two streams into a single token sequence without altering the downstream backbone encoder. Experiments on node classification and link prediction show consistent gains over strong quantized baselines at matched compute, with ablations verifying contributions from hierarchical quantization, adaptive routing, and fusion.

cs.IR↗
arXiv2026

Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification

Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled frameworks for fair data valuation; however, they suffer from exponential computational complexity. We address this challenge by developing efficient algorithms specifically tailored for computing Banzhaf values in $k$-nearest neighbor ($k$NN) classifiers. We first establish the theoretical hardness of the problem by proving that it is \#P-hard. Despite this intractability, we exploit the locality properties of $k$NN classifiers to develop practical exact algorithms. Our main contribution is a dynamic programming framework that achieves significant computational improvements: we present a pseudo-polynomial algorithm with $O(Wkn^2)$ time complexity for weighted $k$NN classifiers, where $W$ is the maximum sum of top-$k$ weights, and a specialized algorithm for unweighted $k$NN that achieves $O(nk^2)$ time complexity, that is, linear in the number of data points. We also offer efficient Monte Carlo estimation methods. Extensive experiments on real-world datasets demonstrate the practical efficiency of our approach and its effectiveness in data valuation applications.

cs.LG↗
arXiv2026

Consistent Tie-Strength Labeling for Multilayer Strong Triadic Closure

Inferring tie strengths (strong vs. weak) is a core task in network analysis, often guided by the Strong Triadic Closure (STC) principle. In multilayer networks, such as social platforms or biological systems, applying STC independently to each layer can lead to inconsistent tie labels, undermining interpretations that rely on coherent relationship semantics across layers. We propose new formulations, multilayer STC and its extension STC+, which are axiomatically grounded and enforce cross-layer consistency. These problems are NP-hard; we present efficient 2- and 6-approximation algorithms alongside exact solutions. Experiments on real-world networks demonstrate that our methods produce consistent tie strength labelings with a transparent structural justification, significantly improving over the baselines.

cs.SI↗
arXiv2026

Top-k on a Budget: Adaptive Ranking with Weak and Strong Oracles

Identifying the top-$k$ items is fundamental but often prohibitive when exact valuations are expensive. We study a two-oracle setting with a fast, noisy weak oracle and a scarce, high-fidelity strong oracle (e.g., human expert verification or expensive simulation). We first analyze a simple screen-then-certify baseline (STC) and prove it makes at most $m(4\varepsilon_{\max})$ strong calls given jointly valid weak confidence intervals with maximum radius $\varepsilon_{\max}$, where $m(\cdot)$ denotes the near-tie mass around the top-$k$ threshold. We establish a conditional lower bound of $Ω(m(\varepsilon_{\max}))$ for any algorithm given the same weak uncertainty. Our main contribution is ACE, an adaptive certification algorithm that focuses strong queries on critical boundary items, achieving the same $O(m(4\varepsilon_{\max}))$ bound while reducing strong calls in practice. We then introduce ACE-W, a fully adaptive two-phase method that allocates weak budget adaptively before running ACE, further reducing strong costs.

cs.LG↗
arXiv2026

Streaming Stochastic Submodular Maximization with On-Demand User Requests

We explore a novel problem in streaming submodular maximization, inspired by the dynamics of news-recommendation platforms. We consider a setting where users can visit a news website at any time, and upon each visit, the website must display up to $k$ news items. User interactions are inherently stochastic: each news item presented to the user is consumed with a certain acceptance probability by the user, and each news item covers certain topics. Our goal is to design a streaming algorithm that maximizes the expected total topic coverage. To address this problem, we establish a connection to submodular maximization subject to a matroid constraint. We show that we can effectively adapt previous methods to address our problem when the number of user visits is known in advance or linear-size memory in the stream length is available. However, in more realistic scenarios where only an upper bound on the visits and sublinear memory is available, the algorithms fail to guarantee any bounded performance. To overcome these limitations, we introduce a new online streaming algorithm that achieves a competitive ratio of $1/(8δ)$, where $δ$ controls the approximation quality. Moreover, it requires only a single pass over the stream, and uses memory independent of the stream length. Empirically, our algorithms consistently outperform the baselines.

cs.DS↗
arXiv2025

TGLib: An Open-Source Library for Temporal Graph Analysis

We initiate an open-source library for the efficient analysis of temporal graphs. We consider one of the standard models of dynamic networks in which each edge has a discrete timestamp and transition time. Recently there has been a massive interest in analyzing such temporal graphs. Common computational data mining and analysis tasks include the computation of temporal distances, centrality measures, and network statistics like topological overlap, burstiness, or temporal diameter. To fulfill the increasing demand for efficient and easy-to-use implementations of temporal graph algorithms, we introduce the open-source library TGLib, which integrates efficient data structures and algorithms for temporal graph analysis. TGLib is highly efficient and versatile, providing simple and convenient C++ and Python interfaces, targeting computer scientists, practitioners, students, and the (temporal) network research community.

cs.DS↗
arXiv2024

An Edge-Based Decomposition Framework for Temporal Networks

A temporal network is a dynamic graph where every edge is assigned an integer time label that indicates at which discrete time step the edge is available. We consider the problem of hierarchically decomposing the network and introduce an edge-based decomposition framework that unifies the core and truss decompositions for temporal networks while allowing us to consider the network's temporal dimension. Based on our new framework, we introduce the $(k,Δ)$-core and $(k,Δ)$-truss decompositions, which are generalizations of the classic $k$-core and $k$-truss decompositions for multigraphs. Moreover, we show how $(k,Δ)$-cores and $(k,Δ)$-trusses can be efficiently further decomposed to obtain spatially and temporally connected components. We evaluate the characteristics of our new decompositions and the efficiency of our algorithms. Moreover, we demonstrate how our $(k,Δ)$-decompositions can be applied to analyze malicious content in a Twitter network to obtain insights that state-of-the-art baselines cannot obtain.

cs.SI↗
arXiv2024

Finding Densest Subgraphs with Edge-Color Constraints

We consider a variant of the densest subgraph problem in networks with single or multiple edge attributes. For example, in a social network, the edge attributes may describe the type of relationship between users, such as friends, family, or acquaintances, or different types of communication. For conceptual simplicity, we view the attributes as edge colors. The new problem we address is to find a diverse densest subgraph that fulfills given requirements on the numbers of edges of specific colors. When searching for a dense social network community, our problem will enforce the requirement that the community is diverse according to criteria specified by the edge attributes. We show that the decision versions for finding exactly, at most, and at least $\textbf{h}$ colored edges densest subgraph, where $\textbf{h}$ is a vector of color requirements, are NP-complete, for already two colors. For the problem of finding a densest subgraph with at least $\textbf{h}$ colored edges, we provide a linear-time constant-factor approximation algorithm when the input graph is sparse. On the way, we introduce the related at least $h$ (non-colored) edges densest subgraph problem, show its hardness, and also provide a linear-time constant-factor approximation. In our experiments, we demonstrate the efficacy and efficiency of our new algorithms.

cs.SI↗
arXiv2024

Inferring Tie Strength in Temporal Networks

Inferring tie strengths in social networks is an essential task in social network analysis. Common approaches classify the ties as wea} and strong ties based on the strong triadic closure (STC). The STC states that if for three nodes, $A$, $B$, and $C$, there are strong ties between $A$ and $B$, as well as $A$ and $C$, there has to be a (weak or strong) tie between $B$ and $C$. A variant of the STC called STC+ allows adding a few new weak edges to obtain improved solutions. So far, most works discuss the STC or STC+ in static networks. However, modern large-scale social networks are usually highly dynamic, providing user contacts and communications as streams of edge updates. Temporal networks capture these dynamics. To apply the STC to temporal networks, we first generalize the STC and introduce a weighted version such that empirical a priori knowledge given in the form of edge weights is respected by the STC. Similarly, we introduce a generalized weighted version of the STC+. The weighted STC is hard to compute, and our main contribution is an efficient 2-approximation (resp. 3-approximation) streaming algorithm for the weighted STC (resp. STC+) in temporal networks. As a technical contribution, we introduce a fully dynamic $k$-approximation for the minimum weighted vertex cover problem in hypergraphs with edges of size $k$, which is a crucial component of our streaming algorithms. An empirical evaluation shows that the weighted STC leads to solutions that better capture the a priori knowledge given by the edge weights than the non-weighted STC. Moreover, we show that our streaming algorithm efficiently approximates the weighted STC in real-world large-scale social networks.

cs.SI↗
arXiv2023

A Higher-Order Temporal H-Index for Evolving Networks

The H-index of a node in a static network is the maximum value $h$ such that at least $h$ of its neighbors have a degree of at least $h$. Recently, a generalized version, the $n$-th order H-index, was introduced, allowing to relate degree centrality, H-index, and the $k$-core of a node. We extend the $n$-th order H-index to temporal networks and define corresponding temporal centrality measures and temporal core decompositions. Our $n$-th order temporal H-index respects the reachability in temporal networks leading to node rankings, which reflect the importance of nodes in spreading processes. We derive natural decompositions of temporal networks into subgraphs with strong temporal coherence. We analyze a recursive computation scheme and develop a highly scalable streaming algorithm. Our experimental evaluation demonstrates the efficiency of our algorithms and the conceptional validity of our approach. Specifically, we show that the $n$-th order temporal H-index is a strong heuristic for identifying super-spreaders in evolving social networks and detects temporally well-connected components.

cs.SI↗
arXiv2023

An Index for Single Source All Destinations Distance Queries in Temporal Graphs

Temporal closeness is a generalization of the classical closeness centrality measure for analyzing evolving networks. The temporal closeness of a vertex $v$ is defined as the sum of the reciprocals of the temporal distances to the other vertices. Ranking all vertices of a network according to the temporal closeness is computationally expensive as it leads to a single-source-all-destination (SSAD) temporal distance query starting from each vertex of the graph. To reduce the running time of temporal closeness computations, we introduce an index to speed up SSAD temporal distance queries called Substream index. We show that deciding if a Substream index of a given size exists is NP-complete and provide an efficient greedy approximation. Moreover, we improve the running time of the approximation using min-hashing and parallelization. Our evaluation with real-world temporal networks shows a running time improvement of up to one order of magnitude compared to the state-of-the-art temporal closeness ranking algorithms.

cs.DB↗
arXiv2022

A Temporal Graphlet Kernel for Classifying Dissemination in Evolving Networks

We introduce the \emph{temporal graphlet kernel} for classifying dissemination processes in labeled temporal graphs. Such dissemination processes can be spreading (fake) news, infectious diseases, or computer viruses in dynamic networks. The networks are modeled as labeled temporal graphs, in which the edges exist at specific points in time, and node labels change over time. The classification problem asks to discriminate dissemination processes of different origins or parameters, e.g., infectious diseases with different infection probabilities. Our new kernel represents labeled temporal graphs in the feature space of temporal graphlets, i.e., small subgraphs distinguished by their structure, time-dependent node labels, and chronological order of edges. We introduce variants of our kernel based on classes of graphlets that are efficiently countable. For the case of temporal wedges, we propose a highly efficient approximative kernel with low error in expectation. We show that our kernels are faster to compute and provide better accuracy than state-of-the-art methods.

cs.SI↗
arXiv2022

Temporal Walk Centrality: Ranking Nodes in Evolving Networks

We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that information does not necessarily spread on shortest paths but on temporal random walks that satisfy the time constraints of the network. We show that temporal walk centrality can identify nodes playing central roles in dissemination processes that might not be detected by related betweenness concepts and other common static and temporal centrality measures. We propose exact and approximation algorithms with different running times depending on the properties of the temporal network and parameters of our new centrality measure. A technical contribution is a general approach to lift existing algebraic methods for counting walks in static networks to temporal networks. Our experiments on real-world temporal networks show the efficiency and accuracy of our algorithms. Finally, we demonstrate that the rankings by temporal walk centrality often differ significantly from those of other state-of-the-art temporal centralities.

cs.SI↗