A Local Updating Algorithm for Personalized PageRank via Chebyshev Polynomials

TL;DR

This paper introduces a distributed algorithm using Chebyshev polynomials for efficiently updating personalized PageRank vectors in dynamic networks, outperforming existing methods in speed and versatility.

Contribution

It presents a novel local update algorithm based on Chebyshev polynomials that improves convergence speed and handles generalized PageRank models without prior algorithms.

Findings

Faster convergence than existing algorithms

Effective in real-world temporal networks

Capable of updating generalized PageRank solutions

Abstract

The personalized PageRank algorithm is one of the most versatile tools for the analysis of networks. In spite of its ubiquity, maintaining personalized PageRank vectors when the underlying network constantly evolves is still a challenging task. To address this limitation, this work proposes a novel distributed algorithm to locally update personalized PageRank vectors when the graph topology changes. The proposed algorithm is based on the use of Chebyshev polynomials and a novel update equation that encompasses a large family of PageRank-based methods. In particular, the algorithm has the following advantages: (i) it has faster convergence speed than state-of-the-art alternatives for local PageRank updating; and (ii) it can update the solution of recent generalizations of PageRank for which no updating algorithms have been developed. Experiments in a real-world temporal network of an autonomous system validate the effectiveness of the proposed algorithm.