覆盖时间、覆盖时间和优化措施
Cover times, blanket times, and majorizing measures
摘要：
我们表现出很强的连接覆盖时间的图，高斯过程，和Talagrand的理论优化措施。特别是，我们证明了任何图$G$的覆盖时间是等价的，直到通用常数，高斯自由场的期望最大值的平方$G$，缩放的边缘数在$G$。这使我们能够解决一些悬而未决的问题。我们给出了一个确定性的多项式时间算法，计算覆盖时间内的O（1）因子的任何图，回答了一个问题的Aldous和Fill（1994）。我们还积极解决了Winkler和Zuckerman（1996）的毯子时间图，表明对于任何图，毯子和覆盖时间都在O（1）因子内。这两个问题的最佳近似因子是$O((\log \log n)^2)$（对于$n$ -顶点图），这是由Kahn、Kim、Lovasz和Vu（2000）提出的。
英文摘要：
We exhibit a strong connection between cover times of graphs, Gaussian processes, and Talagrand's theory of majorizing measures. In particular, we show that the cover time of any graph $G$ is equivalent, up to universal constants, to the square of the expected maximum of the Gaussian free field on $G$, scaled by the number of edges in $G$. This allows us to resolve a number of open questions. We give a deterministic polynomial-time algorithm that computes the cover time to within an O(1) factor for any graph, answering a question of Aldous and Fill (1994). We also positively resolve the blanket time conjectures of Winkler and Zuckerman (1996), showing that for any graph, the blanket and cover times are within an O(1) factor. The best previous approximation factor for both these problems was $O((\log \log n)^2)$ for $n$-vertex graphs, due to Kahn, Kim, Lovasz, and Vu (2000).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
