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Localization of Electrical Flows

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arxiv 1708.01632 v1 pith:PIYPBTBC submitted 2017-08-04 cs.DS cs.DM

Aaron Schild , Satish Rao , Nikhil Srivastava This is my paper · ORCID
classification cs.DScs.DM
keywords electricalflowflowsgraphresultabsoluteaveragecase
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Approximate Spanning Tree Counting from Uncorrelated Edge Sets

    cs.DS 2025-05 conditional novelty 7.0 of 10

    The paper gives an O~(m^1.5 epsilon^-1) time algorithm for approximate spanning tree counting using recursive deletion of uncorrelated edge sets found via electrical-flow localization.

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