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International Workshop on Combinatorial Algorithms

IWOCA 2014: Combinatorial Algorithms pp 110-121 | Cite as

Computing Heat Kernel Pagerank and a Local Clustering Algorithm

  • Fan Chung
  • Olivia SimpsonEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8986)

Abstract

Heat kernel pagerank is a variation of Personalized PageRank given in an exponential formulation. In this work, we present a sublinear time algorithm for approximating the heat kernel pagerank of a graph. The algorithm works by simulating random walks of bounded length and runs in time \(O\big (\frac{\log (\epsilon ^{-1})\log n}{\epsilon ^3\log \log (\epsilon ^{-1})}\big )\), assuming performing a random walk step and sampling from a distribution with bounded support take constant time.

The quantitative ranking of vertices obtained with heat kernel pagerank can be used for local clustering algorithms. We present an efficient local clustering algorithm that finds cuts by performing a sweep over a heat kernel pagerank vector, using the heat kernel pagerank approximation algorithm as a subroutine. Specifically, we show that for a subset S of Cheeger ratio \(\phi \), many vertices in S may serve as seeds for a heat kernel pagerank vector which will find a cut of conductance \(O(\sqrt{\phi })\).

Keywords

Heat kernel pagerank Heat kernel Local algorithms 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.University of California, San DiegoLa JollaUSA

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