Distributed Randomized Algorithms for the PageRank Computation

Abstract

In the search engine of Google, the PageRank algorithm plays a crucial role in ranking the search results. The algorithm quantifies the importance of each web page based on the link structure of the web. We first provide an overview of the original problem setup. Then, we propose several distributed randomized schemes for the computation of the PageRank, where the pages can locally update their values by communicating to those connected by links. The main objective of the paper is to show that these schemes asymptotically converge in the meansquare sense to the true PageRank values. A detailed discussion on the close relations to the multi-agent consensus problems is also given.

Parameter Estimation in a Stochastic System Model for PageRank

“…We suppose that this system depends on an unknown parameter and we prove that the least squares estimator of this parameter is strongly consistent under certain assumptions. Furthermore, motivated by the recent work of Ishii, Tempo, and Bai on distributed randomized PageRank computation [9], [10], [11], [12], we show that the least squares estimator remains strongly consistent within a distributed framework.…”

“…multimedia content such as PDF, image, or video files) are commonplace and introduce columns of zeros in the hyperlink matrix H. Such so-called dangling nodes present a significant obstacle in the computation of PageRank that must be addressed. One straightforward way to circumvent the issue altogether is to give each dangling node an artificial outgoing link back to each page that linked to it [9]. This approach is intuitively justified by the concept of a "back button" (that is, a way of returning from any page to the immediately preceding page), which is a standard feature of modern web browsers.…”

“…In 2010, Ishii and Tempo introduced a distributed randomized approach to PageRank computation [9]. As the name suggests, this method involves the distributed (across all pages in the web) updating of the PageRank vector, where the individual page initiating the update procedure at each time step is selected by a random process that follows a discrete uniform probability distribution.…”

“…wheret ∈ (0, 1) is a modified teleportation parameter that replaces t. We will assume thatt = 2t/(n−t(n−2)), as this value was shown by Ishii and Tempo in [9] to ensure convergence of the distributed update scheme to the true PageRank vector. The original linear system is then replaced by a distributed linear system,…”

A PageRank Algorithm based on Asynchronous Gauss-Seidel Iterations

“…In [7], the authors present a distributed randomized algorithm for the PageRank computation. In [8], by the same authors in a collaboration have studied ergodic randomized algorithms that can be applied to the PageRank problem.…”