AI 中文总结
本文提出VAC采样规则，通过均匀随机生成树减少近似Cholesky分解的填充，保留理论保证并支持线性时间与对数深度并行。
AI 中文摘要
我们提出体积近似Cholesky（VAC），一种用于实用近似Cholesky算法的替代采样规则。我们的规则对产生的乘积团采样一个均匀随机生成树，以减少每一步生成的填充量。采样随机生成树保留了（Kyng & Sachdeva 2016）中可证明正确方案的边边缘分布，同时确保了（Gao, Kyng & Spielman 2023）中提出的实用规则的精神下的连通性。我们的采样方法简单，可证明是线性时间的，并且还支持O(log n)深度的并行实现。
英文摘要
We propose Volume Appproximate Cholesky (VAC), an alternative sampling rule for practical approximate Cholesky algorithms. Our rule samples a uniformly random spanning tree of the arising product clique to reduce the fill-in generated at each step. Sampling a random spanning tree preserves the edgewise marginals of the provably correct scheme of (Kyng \& Sachdeva 2016), while ensuring connectivity in the spirit of the practical rule proposed in (Gao, Kyng \& Spielman 2023). Our sampling method is simple, provably linear time and also admits a $O(\log n)$ depth parallel implementation.
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