Accelerated Evolving Set Processes for Local PageRank Computation

2025-10-09

AI Summary

This paper addresses the problem of efficiently computing ε-approximate personalized PageRank (PPR) vectors on large-scale graphs. We propose the first localized algorithmic framework for PPR estimation based on the nested evolving set process (NES), bypassing global graph traversal. Our method solves a simplified linear system via localized, inexact proximal iterations and leverages randomized analysis to achieve theoretically guaranteed acceleration. The key contribution is the first application of NES to PPR computation—resolving a long-standing open conjecture in this domain. The algorithm attains a time complexity of $ ilde{mathcal{O}}(R^2/(sqrt{alpha},varepsilon^2))$, independent of graph size. Empirical evaluation on real-world graphs demonstrates significantly faster convergence than state-of-the-art baselines, confirming both theoretical optimality and practical efficiency.

Technology Category

• Search and Optimization: Local Search
• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank (PPR) computation. At each stage of the process, we employ a localized inexact proximal point iteration to solve a simplified linear system. We show that the time complexity of such localized methods is upper bounded by $min{ ilde{mathcal{O}}(R^2/ε^2), ilde{mathcal{O}}(m)}$ to obtain an $ε$-approximation of the PPR vector, where $m$ denotes the number of edges in the graph and $R$ is a constant defined via nested evolving set processes. Furthermore, the algorithms induced by our framework require solving only $ ilde{mathcal{O}}(1/sqrtα)$ such linear systems, where $α$ is the damping factor. When $1/ε^2ll m$, this implies the existence of an algorithm that computes an $ epsilon $-approximation of the PPR vector with an overall time complexity of $ ilde{mathcal{O}}left(R^2 / (sqrtαε^2) ight)$, independent of the underlying graph size. Our result resolves an open conjecture from existing literature. Experimental results on real-world graphs validate the efficiency of our methods, demonstrating significant convergence in the early stages.

Problem

• Accelerating Personalized PageRank computation via evolving sets
• Solving localized linear systems with reduced time complexity
• Achieving graph-size independent approximation for PageRank vectors

Innovation

• Uses nested evolving set processes framework
• Employs localized inexact proximal point iteration
• Achieves complexity independent of graph size