Maximum Strong Independent Sets in Hypergraphs: Reductions, Bounds, and Greedy Certificates
Read the original on arXiv Machine Learning →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.
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