再探无向图上的局部PageRank估计：简单且最优
Revisiting Local PageRank Estimation on Undirected Graphs: Simple and Optimal
AI总结：
本研究提出简单最优的BackMC算法用于无向图局部PageRank估计，复杂度优于此前最优结果且达理论下界，在大规模图实验中性能优越。
摘要：
我们提出了一种简单且最优的算法BackMC，用于无向图中的局部PageRank估计：给定包含n个节点和m条边的无向图G中的任意目标节点t，BackMC能准确估计节点t的PageRank得分，同时保证较小的相对误差和较高的成功概率。BackMC的最坏情况计算复杂度上界为$O\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$，其中$d_{\mathrm{min}}$表示G的最小度，$d_t$表示t的度。与此前最优的上界$O\left(\log{n}\cdot \min\left(d_t, m^{1/2}\right)\right)$（VLDB '23，由复杂得多的算法和分析推导得出）相比，我们的BackMC以简单得多的算法将该问题的计算复杂度提升了$\Theta\left(\frac{\log{n}}{d_{\mathrm{min}}}\right)$倍。此外，我们为任何求解局部PageRank估计问题的算法建立了匹配的下界$\Omega\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$，证明了BackMC的理论最优性。我们在各种大规模真实世界图和合成图上开展了大量实验，BackMC始终展现出优越的性能。
英文摘要：
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 $Θ\left(\frac{\log{n}}{d_{\mathrm{min}}}\right)$ with a much simpler algorithm. Furthermore, we establish a matching lower bound of $Ω\left(\frac{1}{d_{\mathrm{min}}}\cdot \min\left(d_t, m^{1/2}\right)\right)$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
