← 研踪 PaperTrailarXiv:2610.06959 · v2
Nearly optimal Personalized PageRank computation
首次提交 2026-10-04 00:15
版本更新 2026-11-03 21:01
雷达观测 2026-11-04 23:39
摘要
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. This problem has a lower bound $Ω(\eps^{-1})$. Working with idealized SDDM solves, 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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v2 · 2026-11-03 21:01 · 最新观测版本
Nearly optimal Personalized PageRank computation
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. This problem has a lower bound $Ω(\eps^{-1})$. Working with idealized SDDM solves, 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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