Spectral Hypergraph Sparsification via Chaining

In a hypergraph on n vertices where D is the maximum size of a hyperedge, there is a weighted hypergraph spectral epsilon-sparsifier with at most O (epsilon(-2) log (D) center dot n log n) hyperedges. This improves over the bound of Kapralov, Krauthgamer, Tardos and Yoshida (2021) who achieve O (epsilon(-4) n(log n)(3)), aswell as the bound O (epsilon(-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).