Maximum Strong Independent Sets in Hypergraphs: Reductions, Bounds, and Greedy Certificates

Abstract:We study the maximum strong independent set problem in a finite hypergraph: find the largest vertex set that intersects every hyperedge in at most one vertex. This objective arises whenever each observed block is a local incompatibility constraint but transitive closure across overlapping blocks is not justified. A motivating example is multi-band LSH-MinHash deduplication, where each collision bucket gives local evidence, while connected-component contraction can impose spurious global equivalences. The paper develops an incidence-structural toolkit for this problem. We prove exact reductions for dominance, incidence twins, and weight-1 blocks; derive closed-form and low-weight upper bounds; introduce puncturing and covering certificates that sharpen those bounds; and analyze a layered greedy clustering algorithm driven by block weights and residual incidence. The algorithmic analysis includes feasibility, maximality, conditional optimality, a layered witness-matching upper bound, and incidence-local complexity bounds. The results give correctness, termination, fixed-point, and optimality certificates for broad incidence families, together with examples showing when different certificates separate or coincide.

Machine Learning (cs.LG)

arXiv:2609.17951 [cs.LG]

(or arXiv:2609.17951v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2609.17951 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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