Efficient Algorithms for Personalized PageRank

TL;DR

This paper introduces a bidirectional algorithm combining linear algebra and Monte Carlo methods that significantly speeds up the estimation of Personalized PageRank scores between node pairs in large graphs, outperforming previous methods.

Contribution

A novel bidirectional algorithm for Personalized PageRank estimation that achieves up to 70x speedup and has provable efficiency and accuracy guarantees.

Findings

70x faster than previous algorithms on diverse graphs

Requires only O(√m) expected time for typical target scores

Provides accurate estimates with theoretical guarantees

Abstract

We present new, more efficient algorithms for estimating random walk scores such as Personalized PageRank from a given source node to one or several target nodes. These scores are useful for personalized search and recommendations on networks including social networks, user-item networks, and the web. Past work has proposed using Monte Carlo or using linear algebra to estimate scores from a single source to every target, making them inefficient for a single pair. Our contribution is a new bidirectional algorithm which combines linear algebra and Monte Carlo to achieve significant speed improvements. On a diverse set of six graphs, our algorithm is 70x faster than past state-of-the-art algorithms. We also present theoretical analysis: while past algorithms require $\Omega(n)$ time to estimate a random walk score of typical size $\frac{1}{n}$ on an $n$-node graph to a given constant accuracy, our algorithm requires only $O(\sqrt{m})$ expected time for an average target, where $m$ is the number of edges, and is provably accurate. In addition to our core bidirectional estimator for personalized PageRank, we present an alternative algorithm for undirected graphs, a generalization to arbitrary walk lengths and Markov Chains, an algorithm for personalized search ranking, and an algorithm for sampling random paths from a given source to a given set of targets. We expect our bidirectional methods can be extended in other ways and will be useful subroutines in other graph analysis problems.