A Sublinear Time Algorithm for PageRank Computations

  • Christian Borgs
  • Michael Brautbar
  • Jennifer Chayes
  • Shang-Hua Teng
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7323)

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.

As part of our analysis, we show that any algorithm for solving this problem must have expected time complexity of \({\Omega}(\frac{n}{\Delta})\). Thus, our algorithm is optimal up to logarithmic factors. Our algorithm (for identifying vertices with significant PageRank) applies a multi-scale sampling scheme that uses a fast personalized PageRank estimator as its main subroutine. For that, we develop a new local randomized algorithm for approximating personalized PageRank which is more robust than the earlier ones developed by Jeh and Widom [9] and by Andersen, Chung, and Lang [2].

Keywords

Local Algorithm Binary Search Tree PageRank Vector Sublinear Time Teleportation Probability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christian Borgs
    • 1
  • Michael Brautbar
    • 2
  • Jennifer Chayes
    • 1
  • Shang-Hua Teng
    • 3
  1. 1.Microsoft Research New EnglandCambridgeUSA
  2. 2.Computer and Information Science DepartmentUniversity of PennsylvaniaPhiladelphiaUSA
  3. 3.Computer Science DepartmentUniversity of Southern CaliforniaLos AngelesUSA

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