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Bidirectional PageRank Estimation: From Average-Case to Worst-Case

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 9479)


We present a new algorithm for estimating the Personalized PageRank (PPR) between a source and target node on undirected graphs, with sublinear running-time guarantees over the worst-case choice of source and target nodes. Our work builds on a recent line of work on bidirectional estimators for PPR, which obtained sublinear running-time guarantees but in an average-case sense, for a uniformly random choice of target node. Crucially, we show how the reversibility of random walks on undirected networks can be exploited to convert average-case to worst-case guarantees. While past bidirectional methods combine forward random walks with reverse local pushes, our algorithm combines forward local pushes with reverse random walks. We also discuss how to modify our methods to estimate random-walk probabilities for any length distribution, thereby obtaining fast algorithms for estimating general graph diffusions, including the heat kernel, on undirected networks.

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  1. 1.

    Specifically, for each node u in the original graph, SALSA creates two virtual nodes, a “consumer-node” \(u'\) and a “producer-node” \(u''\), which are linked by an undirected edge. Any directed edge (uv) is then converted into an undirected edge \((u', v'')\) from u’s consumer node to v’s producer node.

  2. 2.

    Following convention, we use w.h.p. to mean with probability greater than \(1-\frac{1}{n}\).


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Research supported by the DARPA GRAPHS program via grant FA9550-12-1-0411, and by NSF grant 1447697. One author was supported by an NPSC fellowship. Thanks to Aaron Sidford for a helpful discussion.

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Correspondence to Siddhartha Banerjee .

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Lofgren, P., Banerjee, S., Goel, A. (2015). Bidirectional PageRank Estimation: From Average-Case to Worst-Case. In: Gleich, D., Komjáthy, J., Litvak, N. (eds) Algorithms and Models for the Web Graph. WAW 2015. Lecture Notes in Computer Science(), vol 9479. Springer, Cham.

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