Accelerated Evolving Set Processes for Local PageRank Computation
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911233518600192 |
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| author | Huang, Binbin Luo, Luo Xiao, Yanghua Yang, Deqing Zhou, Baojian |
| author_facet | Huang, Binbin Luo, Luo Xiao, Yanghua Yang, Deqing Zhou, Baojian |
| contents | 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 $\min\{\tilde{\mathcal{O}}(R^2/ε^2), \tilde{\mathcal{O}}(m)\}$ 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 $\tilde{\mathcal{O}}(1/\sqrtα)$ such linear systems, where $α$ is the damping factor. When $1/ε^2\ll m$, this implies the existence of an algorithm that computes an $\ epsilon $-approximation of the PPR vector with an overall time complexity of $\tilde{\mathcal{O}}\left(R^2 / (\sqrtαε^2)\right)$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerated Evolving Set Processes for Local PageRank Computation Huang, Binbin Luo, Luo Xiao, Yanghua Yang, Deqing Zhou, Baojian Machine Learning 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 $\min\{\tilde{\mathcal{O}}(R^2/ε^2), \tilde{\mathcal{O}}(m)\}$ 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 $\tilde{\mathcal{O}}(1/\sqrtα)$ such linear systems, where $α$ is the damping factor. When $1/ε^2\ll m$, this implies the existence of an algorithm that computes an $\ epsilon $-approximation of the PPR vector with an overall time complexity of $\tilde{\mathcal{O}}\left(R^2 / (\sqrtαε^2)\right)$, 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. |
| title | Accelerated Evolving Set Processes for Local PageRank Computation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2510.08010 |