The paper investigates the maximum strong independent set problem in finite hypergraphs, where the goal is to find the largest vertex set that intersects each hyperedge in at most one vertex. It introduces an incidence-structural toolkit, proving exact reductions for dominance, incidence twins, and weight‑1 blocks, and derives closed‑form and low‑weight upper bounds. The authors also present puncturing and covering certificates that refine these bounds and analyze a layered greedy clustering algorithm driven by block weights and residual incidence, providing feasibility, maximality, conditional optimality, and incidence‑local complexity guarantees.
arXiv:2609. 30477v1 Announce Type: cross Abstract: Exact Euclidean \(K\)-means partitions \(n\) observations into \(K\) unlabelled clusters, but the unrestricted search is generally exponential.
arXiv:2608. 03171v1 Announce Type: cross Abstract: We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations.
arXiv:2608.29635v1 Announce Type: new Abstract: We study unsupervised hypergraph alignment, where the goal is to infer node correspondences between two hypergraphs using only structural information,...
arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.
arXiv:2412. 03008v2 Announce Type: replace-cross Abstract: Local/seeded clustering aims to find a compact cluster near the given starting instances.
arXiv:2602. 16807v2 Announce Type: replace Abstract: A collection of hyperplanes $\mathcal{H}$ slices all edges of the $n$-dimensional hypercube $Q_n$ with vertex set $\{-1,1\}^n$ if, for every edge $e$ in the hypercube, there exists a hyperplane in $\mathcal{H}$ intersecting $e$ in its interior.
arXiv:2608. 16315v1 Announce Type: cross Abstract: Correlation clustering is a fundamental unsupervised learning problem.
arXiv:2607. 13217v1 Announce Type: cross Abstract: Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton.
arXiv:2602. 21312v4 Announce Type: replace-cross Abstract: This work considers a number of optimization problems and reductive relations between them.
The maximum independent set (MIS) problem is a fundamental NP-hard combinatorial optimization problem with applications in scheduling, resource allocation, and network analysis. Exact solvers can prov...
Consider the following variation on the Hierarchical Clustering problem: Usually, while building a hierarchical clustering, one recursively partitions the data until each cluster becomes a singleton. We relax the halting condition of the recursive process to stop whenever the remaining cluster is a graph belonging to a class $\mathcal{F}$.
arXiv:2608. 08154v1 Announce Type: cross Abstract: The Zarankiewicz number Z(m,n,s,t) is the maximum number of edges in a bipartite graph with parts of orders m and n containing no copy of Ks,t.