### Estimating PageRank on graph streamsEstimating PageRank on graph streams

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 Author Sarma, Atish Das ♦ Gollapudi, Sreenivas ♦ Panigrahy, Rina Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2011 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Algorithms ♦ PageRank ♦ Graph conductance ♦ Mixing time ♦ Random walk ♦ Streaming algorithms Abstract This article focuses on computations on large graphs (e.g., the web-graph) where the edges of the graph are presented as a stream. The objective in the streaming model is to use small amount of memory (preferably sub-linear in the number of nodes $\textit{n})$ and a smaller number of passes. In the streaming model, we show how to perform several graph computations including estimating the probability distribution after a random walk of length $\textit{l},$ the mixing time $\textit{M},$ and other related quantities such as the conductance of the graph. By applying our algorithm for computing probability distribution on the web-graph, we can estimate the $\textit{PageRank}$ $\textit{p}$ of any node up to an additive error of &sqrt;ε $\textit{p}+ε$ in $\textit{Õ}(&sqrt;\textit{M}/α)$ passes and $\textit{Õ}(min(\textit{n}α+1/ε&sqrt;\textit{M}/α+(1/ε)\textit{M}α,$ α $\textit{n}&sqrt;\textit{M}α$ + $(1/ε)&sqrt;\textit{M}/α))$ space, for any α ∈ (0,1]. Specifically, for ε = $\textit{M}/\textit{n},$ α = $M^{™1/2},$ we can compute the approximate PageRank values in $Õ(nM^{™1/4})$ space and $Õ(M^{3/4})$ passes. In comparison, a standard implementation of the PageRank algorithm will take $\textit{O(n)}$ space and $\textit{O(M)}$ passes. We also give an approach to approximate the PageRank values in just Õ(1) passes although this requires $Õ(\textit{nM})$ space. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2011-06-09 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 58 Issue Number 3 Page Count 19 Starting Page 1 Ending Page 19

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Source: ACM Digital Library