加速PageRank计算中的局部推送原语
Accelerating the Local Push Primitive for PageRank Computation
- Renmin University of China（中国人民大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出加速局部推送原语，将PageRank近似计算时间从O(1/(αε))降至Õ(1/(√αε))，并解决ℓ1正则化PageRank的开放问题，通过势函数分析改进活跃集方法，可加速局部图聚类和有效电阻估计。
AI中文摘要：
我们提出了一种局部算法，在Andersen、Chung和Lang（ACL；Internet Math. 2007）的意义下，以传送参数α计算ε近似PageRank向量，其时间复杂度为Õ(1/(√α·ε))，且具有高概率保证，改进了原始局部推送方法的O(1/(αε))运行时间。我们的方法同样适用于ℓ1正则化PageRank问题，对于正则化参数ρ，运行时间为Õ(1/(√α·ρ))，从而对Fountoulakis和Yang（COLT 2022）提出的开放问题给出了肯定回答。我们更快的原语有望改进大量依赖局部推送的图算法。例如，将我们的原语替换到ACL框架中，直接产生更快的基于PageRank的局部图聚类算法；我们还开发了归约方法，从而得到更快的有效电阻估计算法。我们的主要技术贡献是对Wei和Yang（预印本2026）的活跃集方法改进版进行了势函数分析，该方法反复在当前活跃节点集上调用SDD求解器并扩展该集合。我们关联连续扩展块上的势能下降，证明扩展次数以Õ(1/√α)为界。
英文摘要：
We propose a local algorithm that computes an $\varepsilon$-approximate PageRank vector in the sense of Andersen, Chung, and Lang (ACL; Internet Math. 2007) with teleportation parameter $α$ in $\widetilde{O}\bigl(1 / \bigl(\sqrtα \, \varepsilon\bigr)\bigr)$ time with high probability, improving the $O\bigl(1/(α\varepsilon)\bigr)$ running time of their original local push method. Our method also applies to the $\ell_1$-regularized PageRank problem with a running time of $\widetilde{O}\bigl(1 / \bigl(\sqrtα \, ρ\bigr)\bigr)$ for regularization parameter $ρ$, giving a positive answer to the open problem posed by Fountoulakis and Yang (COLT 2022). Our faster primitive has the potential to improve a broad range of graph algorithms that rely on local push. For example, substituting our primitive into the ACL framework directly yields faster PageRank-based local graph clustering, and we also develop reductions that lead to faster algorithms for effective resistance estimation. Our main technical contribution is a potential-function analysis of a refinement of the active-set method of Wei and Yang (preprint 2026), which repeatedly invokes an SDD solver on the current active set of nodes and expands the set. We relate the potential decreases over consecutive blocks of expansions to show that the number of expansions is bounded by $\widetilde{O}\bigl(1 / \sqrtα\bigr)$.
