A Sublinear Time Algorithm for PageRank Computations

Christian Borgs, Michael Brautbar, Jennifer T. Chayes, Shang-Hua Teng

Abstract: In a network, identifying all vertices whose PageRank is more than a given threshold value Δ is a basic problem that has arisen in Web and social network analyses. In this paper, we develop a nearly optimal, sublinear time, randomized algorithm for a close variant of this problem. When given a directed network G = (V,E), a threshold value Δ, and a positive constant c > 3, with probability 1 − o(1), our algorithm will return a subset S ⊆ V with the property that S contains all vertices of PageRank at least Δ and no vertex with PageRank less than Δ/c. The running time of our algorithm is always \(\tilde{O}(\frac{n}{\Delta})\). In addition, our algorithm can be efficiently implemented in various network access models including the Jump and Crawl query model recently studied by [6], making it suitable for dealing with large social and information networks.