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