Abstract. 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 worstcase 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 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. Whether such worst-case running-time results extend to general graphs, or if PageRank computation is fundamentally easier on undirected graphs as opposed to directed graphs, remains an open question.
Similar bounds can be found in REF for Personalized PageRank on undirected graphs.
Bidirectional PageRank Estimation: From Average-Case to Worst-Case
ArXiv
ArXiv
Mathematics Computer Science