Revisiting Local PageRank Estimation on Undirected Graphs: Simple and Optimal

TL;DR

This paper introduces BackMC, a simple and optimal algorithm for local PageRank estimation in undirected graphs, achieving the best possible complexity and outperforming previous methods both theoretically and empirically.

Contribution

The paper presents BackMC, a new algorithm with proven optimal complexity for local PageRank estimation, simplifying previous approaches and establishing matching lower bounds.

Findings

BackMC achieves optimal worst-case complexity.

BackMC outperforms previous algorithms in experiments.

Theoretical lower bounds confirm BackMC's optimality.

Abstract

We propose a simple and optimal algorithm, BackMC, for local PageRank estimation in undirected graphs: given an arbitrary target node $t$ in an undirected graph $G$ comprising $n$ nodes and $m$ edges, BackMC accurately estimates the PageRank score of node $t$ while assuring a small relative error and a high success probability. The worst-case computational complexity of BackMC is upper bounded by $O\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$, where $d_{\mathrm{min}}$ denotes the minimum degree of $G$, and $d_t$ denotes the degree of $t$, respectively. Compared to the previously best upper bound of $ O\left(\log{n}\cdot \min\left(d_t, m^{1/2}\right)\right)$ (VLDB '23), which is derived from a significantly more complex algorithm and analysis, our BackMC improves the computational complexity for this problem by a factor of $\Theta\left(\frac{\log{n}}{d_{\mathrm{min}}}\right)$ with a much simpler algorithm. Furthermore, we establish a matching lower bound of $\Omega\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$ for any algorithm that attempts to solve the problem of local PageRank estimation, demonstrating the theoretical optimality of our BackMC. We conduct extensive experiments on various large-scale real-world and synthetic graphs, where BackMC consistently shows superior performance.