Accelerated Evolving Set Processes for Local PageRank Computation

• URL: http://arxiv.org/abs/2510.08010v4
• Date: Mon, 27 Oct 2025 02:38:07 GMT
• Title: Accelerated Evolving Set Processes for Local PageRank Computation
• Authors: Binbin Huang, Luo Luo, Yanghua Xiao, Deqing Yang, Baojian Zhou,
• Abstract summary: This work proposes a novel framework based on nested evolving set processes to accelerate Personalized PageRank computation.<n>We show that the time complexity of such localized methods is upper bounded by $mintildemathcalO(R2/epsilon2), tildemathcalO(m)$ to obtain an $epsilon$-approximation of the PPR vector.
• Score: 75.54334100808022
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $\min\{\tilde{\mathcal{O}}(R^2/\epsilon^2), \tilde{\mathcal{O}}(m)\}$ to obtain an $\epsilon$-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 $\tilde{\mathcal{O}}(1/\sqrt{\alpha})$ such linear systems, where $\alpha$ is the damping factor. When $1/\epsilon^2\ll m$, this implies the existence of an algorithm that computes an $\ epsilon $-approximation of the PPR vector with an overall time complexity of $\tilde{\mathcal{O}}\left(R^2 / (\sqrt{\alpha}\epsilon^2)\right)$, 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.

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