Estimating PageRank on graph streams

Abstract

This study 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 n) and a few passes.In the streaming model, we show how to perform several graph computations including estimating the probability distribution after a random walk of length l, mixing time, and the conductance. We estimate the mixing time M of a random walk in O(nα+Mα√n+√Mn/α) space and O(√Mα) passes. Furthermore, the relation between mixing time and conductance gives us an estimate for the conductance of the graph. By applying our algorithm for computing probability distribution on the web-graph, we can estimate the PageRank p of any node up to an additive error of √ep in O(√M/α) passes and O(min(nα + 1/e √M/α + 1/e Mα, αn√Mα + 1/e √M/α)) space, for any α ∈ (0, 1]. In particular, for e = M/n, by setting α = M--1/2, we can compute the approximate PageRank values in O(nM--1/4) space and O(M3/4) passes. In comparison, a standard implementation of the PageRank algorithm will take O(n) space and O(M) passes.