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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 $O(\log^2 n)$.
Minimizing congestion in general networks
Harald Racke · 2002
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Daniel A Spielman and Shang-Hua Teng · 2004
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Minimizing average latency in oblivious routing
Prahladh Harsha, Thomas P Hayes, Hariharan Narayanan, Harald Räcke, and Jaikumar Radhakrishnan · 2008
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Faster generation of random spanning trees
Jonathan A Kelner and Aleksander Madry · 2009
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Mixing times and l p bounds for oblivious routing
Gregory Lawler and Hariharan Narayanan · 2009
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Electrical flows, laplacian systems, and faster approximation of maximum flow in undirected graphs
Paul Christiano, Jonathan A Kelner, Aleksander Madry, Daniel A Spielman, and Shang-Hua Teng · 2011
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Jonathan Kelner and Petar Maymounkov · 2011
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Daniel A Spielman and Nikhil Srivastava · 2011
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Faster approximate multicommodity flow using quadratically coupled flows
Jonathan A Kelner, Gary L Miller, and Richard Peng · 2012
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Modern graph theory
Béla Bollobás · 2013
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A new approach to computing maximum flows using electrical flows
Yin Tat Lee, Satish Rao, and Nikhil Srivastava · 2013
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Navigating central path with electrical flows: From flows to matchings, and back
Aleksander Madry · 2013
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Fast generation of random spanning trees and the effective resistance metric
Aleksander Madry, Damian Straszak, and Jakub Tarnawski · 2015
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Approximate gaussian elimination for laplacians: Fast, sparse, and simple
Rasmus Kyng and Sushant Sachdeva · 2016
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Probability on Trees and Networks
Russell Lyons and Yuval Peres · 2016
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Sampling random spanning trees faster than matrix multiplication
David Durfee, Rasmus Kyng, John Peebles, Anup B Rao, and Sushant Sachdeva · 2017
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