Nearly optimal Personalized PageRank computation

2026-10-03

AI Summary

This study addresses the computational bottleneck in personalized PageRank (PPR) estimation on undirected, unweighted graphs, where conventional approaches depend on the teleportation parameter α, thereby limiting efficiency. To overcome this limitation, this work proposes an improved local push algorithm integrated with advanced graph-theoretic analysis techniques to optimize approximate vector computation and eliminate the dependence on α. Notably, this research achieves the first reduction of PPR computational complexity from O((αε)⁻¹) to O(ε^{-1-o(1)}) under absolute error guarantees, yielding near-optimal PPR estimation. Building upon these theoretical advances, the authors further design a near-linear-time local graph clustering scheme whose complexity is independent of the graph conductance φ.

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 $φ$.

Problem

• Personalized PageRank
• local graph clustering
• error guarantee
• time complexity

Innovation

• Personalized PageRank
• local push method
• nearly optimal algorithm
• local graph clustering
• ACL error guarantee