Estimating Single-Node PageRank in $\tilde{O}\left(\min\{d_t, \sqrt{m}\}\right)$ Time

TL;DR

This paper introduces SetPush, a new algorithm that estimates a node's PageRank in undirected graphs within near-optimal time complexity, significantly improving efficiency over previous methods.

Contribution

The paper presents SetPush, a novel algorithm achieving near-optimal sublinear time complexity for single-node PageRank estimation on undirected graphs.

Findings

SetPush achieves $ ilde{O}( ext{min}igrace{d_t, \sqrt{m}igrace})$ time complexity.

Experimental results demonstrate the effectiveness of SetPush.

SetPush outperforms existing methods in efficiency for undirected graphs.

Abstract

PageRank is a famous measure of graph centrality that has numerous applications in practice. The problem of computing a single node's PageRank has been the subject of extensive research over a decade. However, existing methods still incur large time complexities despite years of efforts. Even on undirected graphs where several valuable properties held by PageRank scores, the problem of locally approximating the PageRank score of a target node remains a challenging task. Two commonly adopted techniques, Monte-Carlo based random walks and backward push, both cost $O(n)$ time in the worst-case scenario, which hinders existing methods from achieving a sublinear time complexity like $O(\sqrt{m})$ on an undirected graph with $n$ nodes and $m$ edges. In this paper, we focus on the problem of single-node PageRank computation on undirected graphs. We propose a novel algorithm, SetPush, for estimating single-node PageRank specifically on undirected graphs. With non-trival analysis, we prove that our SetPush achieves the $\tilde{O}\left(\min\left\{d_t, \sqrt{m}\right\}\right)$ time complexity for estimating the target node $t$'s PageRank with constant relative error and constant failure probability on undirected graphs. We conduct comprehensive experiments to demonstrate the effectiveness of SetPush.