Online Algorithms for Spectral Hypergraph Sparsification

Explore a 32-minute lecture on online algorithms for spectral hypergraph sparsification presented by Yuichi Yoshida from the National Institute of Informatics at the Simons Institute. Delve into the first online algorithm for spectral hypergraph sparsification, where hyperedges with positive weights arrive in a stream, requiring immediate decisions on inclusion in the sparsifier. Discover how this algorithm produces an (ϵ,δ)-spectral sparsifier with multiplicative error ϵ and additive error δ, achieving O(ϵ^{-2} n log n log r log(1+ϵW/δn)) hyperedges with high probability. Learn about the significant space complexity improvement, from Ω(m) in previous algorithms to O(n2), offering an exponential reduction since m can be exponential in n. Gain insights into this groundbreaking work, based on collaborative research with Tasuku Soma and Kam Chuen Tung, as part of the Sublinear Graph Simplification series.