Local Algorithms for Estimating Effective Resistance

• URL: http://arxiv.org/abs/2106.03476v1
• Date: Mon, 7 Jun 2021 10:08:12 GMT
• Title: Local Algorithms for Estimating Effective Resistance
• Authors: Pan Peng, Daniel Lopatta, Yuichi Yoshida, Gramoz Goranci
• Abstract summary: In this work, we design several emphlocal algorithms for estimating effective resistances on massive graphs. Our main algorithm approximates the effective resistance between any vertices pair $s,t$ with an arbitrarily small additive error. We perform an extensive empirical study on several benchmark datasets, validating our algorithms.
• Score: 26.54556748340991
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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