发表机构
School of Computer Science, Beijing Institute of Technology（北京理工大学计算机学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种消除对传送参数依赖的算法，在O(ε^{-1-o(1)})时间内实现ACL误差保证的个性化PageRank计算，并得到复杂度与φ无关的近乎线性局部图聚类算法。
AI 中文摘要
我们研究了在无向且无权图$G$上计算个性化PageRank（PPR）这一基本问题。我们关注由Andersen、Chung和Lang [ACL; FOCS 2006 和 Internet Math 2007]引入的$\eps$-误差保证。他们经典的局部推送方法在$O((\alpha\eps)^{-1})$时间内计算出满足ACL $\eps$-误差保证的近似PPR向量，其中$\alpha$是传送参数。在本文中，我们消除了对$\alpha$的依赖，并提出了一种在$O(\eps^{-1-o(1)})$时间内达到相同误差保证的算法。因此，我们在ACL误差保证下获得了近乎最优的PPR计算算法，以及一个复杂度与$\phi$无关的近乎线性的局部图聚类算法。
英文摘要
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 $ϕ$.
