Spectral hypergraph sparsification via chaining
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In a hypergraph on n vertices where D is the maximum size of a hyperedge, there is a weighted hypergraph spectral ε-sparsifier with at most O(ε^-2log(D) · n log n) hyperedges. This improves over the bound of Kapralov, Krauthgamer, Tardos and Yoshida (2021) who achieve O(ε^-4 n (log n)^3), as well as the bound O(ε^-2 D^3 n log n) obtained by Bansal, Svensson, and Trevisan (2019). The same sparsification result was obtained independently by Jambulapati, Liu, and Sidford (2022).
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