Effective resistance is an important metric that measures the similarity of two vertices in a graph. It has found applications in graph clustering, recommendation systems and network reliability, among others. In spite of the importance of the effective resistances, we still lack efficient algorithms to exactly compute or approximate them on massive graphs. In this work, we design several \emph{local algorithms} for estimating effective resistances, which are algorithms that only read a small portion of the input while still having provable performance guarantees. To illustrate, our main algorithm approximates the effective resistance between any vertex pair $s,t$ with an arbitrarily small additive error $\varepsilon$ in time $O(\mathrm{poly}(\log n/\varepsilon))$, whenever the underlying graph has bounded mixing time. We perform an extensive empirical study on several benchmark datasets, validating the performance of our algorithms.

翻译：有效阻力是测量图中两个顶点相似性的重要衡量标准。 它在图形群集、 推荐系统和网络可靠性中发现应用程序。 尽管有效阻力很重要, 我们仍然缺乏精确计算或接近巨幅图的高效算法。 在这项工作中, 我们设计了数种计算有效阻力的算法, 这些算法只读取输入的一小部分, 但仍有可辨识的性能保证。 为了说明这一点, 我们的主要算法比较了任何顶点对美元之间的有效阻力, 以及任意的小添加错误( $\ varepsilon$ ), 时间为$O (\ mathrm{poly} (\log n/\ varepsilon)) 。 只要基本图将混合时间捆绑在一起, 我们就会对几个基准数据集进行广泛的实验研究, 验证我们的算法的性能 。