Convergence of Distributed Randomized PageRank Algorithms

TL;DR

This paper proves that distributed randomized PageRank algorithms, which update page importance scores through local communication, converge almost surely to the true PageRank values using stochastic approximation techniques.

Contribution

It establishes the almost sure convergence of DRPA to true PageRank values under iid randomization assumptions, providing theoretical validation for these algorithms.

Findings

DRPA converges almost surely to true PageRank

Convergence is proven using stochastic approximation methods

Supports the effectiveness of distributed PageRank computations

Abstract

The PageRank algorithm employed by Google quantifies the importance of each page by the link structure of the web. To reduce the computational burden the distributed randomized PageRank algorithms (DRPA) recently appeared in literature suggest pages to update their ranking values by locally communicating with the linked pages. The main objective of the note is to show that the estimates generated by DRPA converge to the true PageRank value almost surely under the assumption that the randomization is realized in an independent and identically distributed (iid) way. This is achieved with the help of the stochastic approximation (SA) and its convergence results.