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arXiv · 2610.06959

Nearly optimal Personalized PageRank computation

Rong-Hua Li·Yichun Yang·Junjie Zhou
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Abstract

We study the fundamental problem of computing Personalized PageRank (PPR) on an undirected and unweighted graph $G$. We focus on the $\eps$-error guarantee introduced by Andersen, Chung, and Lang [ACL; FOCS 2006 $\&$ Internet Math 2007]. Their classic local push method computes an approximate PPR vector satisfying the ACL $\eps$-error guarantee in $O((α\eps)^{-1})$ time, where $α$ is the teleportation parameter. In this paper, we eliminate the dependence on $α$ and present an algorithm that achieves the same error guarantee in $O(\eps^{-1-o(1)})$ time. Consequently, we obtain a nearly optimal algorithm for PPR computation under the ACL error guarantee, and a nearly linear algorithm for local graph clustering with complexity independent of $ϕ$.

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Rong-Hua Li, Yichun Yang, Junjie Zhou. 2026-10-03. Nearly optimal Personalized PageRank computation. https://arxiv.org/abs/2610.06959

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