The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Scaling personalized web search
WWW '03 Proceedings of the 12th international conference on World Wide Web
Topic-Sensitive PageRank: A Context-Sensitive Ranking Algorithm for Web Search
IEEE Transactions on Knowledge and Data Engineering
Local Graph Partitioning using PageRank Vectors
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Monte Carlo Methods in PageRank Computation: When One Iteration is Sufficient
SIAM Journal on Numerical Analysis
Spectral methods for matrices and tensors
Proceedings of the forty-second ACM symposium on Theory of computing
SIAM Journal on Discrete Mathematics
The power of local information in PageRank
Proceedings of the 22nd international conference on World Wide Web companion
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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 c3, 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].