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October 1, 2025Open Access

Near-optimal Hypergraph Sparsification in Insertion-only and Bounded-deletion Streams

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This research demonstrates a space-efficient hypergraph cut-sparsifier in insertion-only streams, indicating lower complexity than dynamic streams.

A $(1 ext{epsilon})$ cut-sparsifier can be computed in $ ilde{O}(nr/ ext{epsilon}^2)$ bits of space.
Previous methods for dynamic streams required $ ilde{O}(nr ext{log} m/ ext{epsilon}^2)$ bits of space.
The study positions hypergraph sparsification in insertion-only streams on par with the static case.
The results highlight a $ ext{Omega}( ext{log} m)$ factor separation in space complexity between the two models.

Khanna et al. (2025) studied this question.

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This research demonstrates a space-efficient hypergraph cut-sparsifier in insertion-only streams, indicating lower complexity than dynamic streams.