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arXiv · 1708.01632

Localization of Electrical Flows

Aaron Schild·Satish Rao·Nikhil Srivastava
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Abstract

We show that in any graph, the average length of a flow path in an electrical flow between the endpoints of a random edge is $O(\log^2 n)$. This is a consequence of a more general result which shows that the spectral norm of the entrywise absolute value of the transfer impedance matrix of a graph is $O(\log^2 n)$. This result implies a simple oblivious routing scheme based on electrical flows in the case of transitive graphs.

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Aaron Schild, Satish Rao, Nikhil Srivastava. 2017-08-04. Localization of Electrical Flows. https://arxiv.org/abs/1708.01632

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