arXiv subjects

Lutz Oettershagen

Publications and source records attributed to Lutz Oettershagen.

3 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↗