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 $O(\varepsilon^{-2} \log(D) \cdot n \log n)$ 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 $O(\varepsilon^{-2} D^3 n \log n)$ obtained by Bansal, Svensson, and Trevisan (2019). The same sparsification result was obtained independently by Jambulapati, Liu, and Sidford (2022).

翻译：在以美元为最高值的顶端顶端的顶端高压图中,以美元为最高值的顶端,有一个加权高射线光谱 $\varepsilon$-spariter,最多为 O(\\ varepsilon}_2}\log(D)\cdn\log n\log nn)$的顶端。这改善了Kapralov、Krauthgamer、Tardos和Yoshida(2021年)的界限,这些高射线光谱光谱光谱 $(\ varepsilon}_2} D}3 n\log n) 美元,由Bansal、Svensson和Trevisan(2019年)获得。同样的水晶化结果是由Jambulapati、Lu和Sidford(2022年)独立取得的。