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 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 𝜀 in time 𝑂 (poly(log 𝑛/𝜀)), whenever the underlying graph has bounded mixing time. We perform an extensive empirical study on several benchmark datasets, validating the performance of our algorithms.
CCS CONCEPTS• Mathematics of computing → Graph algorithms; • Theory of computation → Sketching and sampling.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.