Computing heat kernel pagerank and a local clustering algorithm

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.

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