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arXiv 1208.3071cs.DCcs.DS
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快速分布式PageRank计算

Fast Distributed PageRank Computation

Atish Das Sarma, Anisur Rahaman Molla, Gopal Pandurangan, Eli Upfal

摘要:

在过去的十年中,PageRank在广泛的应用程序和领域中获得了重要性,自从它首次被证明可以有效地确定大型图中的节点重要性(并且是Google搜索引擎背后的先驱思想)。在单独的分布式计算中,PageRank向量或更一般地基于随机游走的量已经用于范围从确定重要节点、负载均衡、搜索和识别连接结构的若干不同应用。然而,令人惊讶的是,设计可证明有效的全分布式算法来计算PageRank的工作很少。困难在于,由于通信带宽限制和收敛速率,传统的矩阵-向量乘法风格的迭代法可能并不总是很好地适应分布式设置。在本文中,我们提出了快速的随机行走为基础的分布式算法计算PageRanks在一般的图,并证明了强界轮复杂度。我们首先提出了一种分布式算法,它在任何图(有向或无向)上以高概率进行$O\big(\log n/\eps \big)$轮,其中$n$是网络大小,$\eps$是PageRank计算中使用的重置概率(通常$\eps$是固定常数)。然后,我们提出了一个更快的算法,需要$O\big(\sqrt{\log n}/\eps \big)$轮无向图。上述两种算法都是可缩放的,因为每个节点在每个轮的每个边缘上仅发送少量($\polylog n$)比特。据我们所知,这是第一个完全分布式的计算PageRank向量的算法,可证明运行时间有效。

英文摘要:

Over the last decade, PageRank has gained importance in a wide range of applications and domains, ever since it first proved to be effective in determining node importance in large graphs (and was a pioneering idea behind Google's search engine). In distributed computing alone, PageRank vector, or more generally random walk based quantities have been used for several different applications ranging from determining important nodes, load balancing, search, and identifying connectivity structures. Surprisingly, however, there has been little work towards designing provably efficient fully-distributed algorithms for computing PageRank. The difficulty is that traditional matrix-vector multiplication style iterative methods may not always adapt well to the distributed setting owing to communication bandwidth restrictions and convergence rates. In this paper, we present fast random walk-based distributed algorithms for computing PageRanks in general graphs and prove strong bounds on the round complexity. We first present a distributed algorithm that takes $O\big(\log n/\eps \big)$ rounds with high probability on any graph (directed or undirected), where $n$ is the network size and $\eps$ is the reset probability used in the PageRank computation (typically $\eps$ is a fixed constant). We then present a faster algorithm that takes $O\big(\sqrt{\log n}/\eps \big)$ rounds in undirected graphs. Both of the above algorithms are scalable, as each node sends only small ($\polylog n$) number of bits over each edge per round. To the best of our knowledge, these are the first fully distributed algorithms for computing PageRank vector with provably efficient running time.

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。

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