1. A Sublinear Time Algorithm for PageRank Computations CHRISTIA N BORGS MICHAEL BRAUTBA R JENNIFER CHAYES SHANG- HUA TENG

2. Motivation o Identify the set of graph vertices that are “significant” o Examples ◦ Social advertising ◦ Web search

3. PageRank o A method for rating the importance of web pages objectively and mechanically utilizing the link structure of the web o Proportional to the probability that a page is visited by a random surfer who explores the web o PageRank was developed at Stanford University by Larry Page and Sergey Brin in 1996

4. Basics

5. Simple Example

6. The Problem with the Basic Model

7. An Improved Model

8. Personalized PageRank

9. Useful Equations

10. Significant PageRank

11. Local Robust Computation of Personalized PageRank APPROXROW ALGORITHM

12. ApproxRow Algorithm

14. Number of Queries

15. Observation

16. Correctness

17. Correctness(2)

18. Multi-Scale PPR Matrix Sampling and Significant PageRank APPROXIMATE PAGE RANK ALGORITHM

19. Main Idea

20. Assumptions o We assume that all the values returned by ApproxRow are exact ◦ Removing this assumption will affect the approximation by only a multiplicative factor of 3 o We present the algorithm for c=4 but it can be easily extended for any c>3

22. Correctness

23. Correctness(2)

24. Number of Queries