Chaining, Group Leverage Score Overestimates, and Fast Spectral Hypergraph Sparsification

09/21/2022

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by   Arun Jambulapati, et al.

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We present an algorithm that given any n-vertex, m-edge, rank r hypergraph constructs a spectral sparsifier with O(n ε^-2log n log r) hyperedges in nearly-linear O(mr) time. This improves in both size and efficiency over a line of work (Bansal-Svensson-Trevisan 2019, Kapralov-Krauthgamer-Tardos-Yoshida 2021) for which the previous best size was O(min{n ε^-4log^3 n,nr^3 ε^-2log n}) and runtime was O(mr + n^O(1)). Independent Result: In an independent work, Lee (Lee 2022) also shows how to compute a spectral hypergraph sparsifier with O(n ε^-2log n log r) hyperedges.