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 varepsilon-sparsifier with at most O(varepsilon-2 log(D) · n log n) hyperedges. This improves over the bound of Kapralov, Krauthgamer, Tardos and Yoshida (2021) who achieve O(varepsilon-4 n (log n)3), as well as the bound O(varepsilon-2 D3 n log n) obtained by Bansal, Svensson, and Trevisan (2019). The same sparsification result was obtained independently by Jambulapati, Liu, and Sidford (2022).