arXiv 1006.28802010-06cs.DScs.DBcs.IR

快速增量和个性化PageRank

Fast Incremental and Personalized PageRank

Bahman Bahmani, Abdur Chowdhury, Ashish Goel

摘要：

在本文中，我们分析了效率的Monte Carlo方法的增量计算PageRank，个性化PageRank，和类似的随机游走为基础的方法（专注于SALSA），在大规模的动态发展的社交网络。我们假设友谊图存储在分布式共享内存中，就像Twitter这样的大型社交网络一样。对于全局PageRank，我们假设社交网络具有$n$节点，并且$m$逆向选择的边以随机顺序到达。我们表明，重置概率$ε$，总的工作需要保持一个准确的估计（使用蒙特卡罗方法）的PageRank的每个节点在任何时候是$O(\frac{n\ln m}{ε^{2}})$。这明显优于所有已知的递增PageRank的界限。例如，如果我们在每个边到达时简单地重新计算PageRank，则简单幂迭代方法需要$Ω(\frac{m^2}{\ln(1/(1-ε))})$总时间，而Monte Carlo方法需要$O(mn/ε)$总时间;两者都非常昂贵。此外，我们还表明，我们可以同样有效地处理删除。然后，我们研究了从种子节点开始的顶级$k$个性化PageRank的计算，假设个性化PageRank遵循指数为$α< 1$的幂律。我们表明，如果我们存储从每个节点开始的$R>q\ln n$随机游走足够大的常数$q$（使用全局PageRank概述的方法），那么对分布式社交网络数据库的调用的预期数量是$O(k/(R^{(1-α)/α}))$。我们还提出了实验结果，从社交网站，Twitter，验证我们的假设和分析。总体结果是，该算法对于动态社交网络上的实时查询来说足够快。

英文摘要：

In this paper, we analyze the efficiency of Monte Carlo methods for incremental computation of PageRank, personalized PageRank, and similar random walk based methods (with focus on SALSA), on large-scale dynamically evolving social networks. We assume that the graph of friendships is stored in distributed shared memory, as is the case for large social networks such as Twitter. For global PageRank, we assume that the social network has $n$ nodes, and $m$ adversarially chosen edges arrive in a random order. We show that with a reset probability of $ε$, the total work needed to maintain an accurate estimate (using the Monte Carlo method) of the PageRank of every node at all times is $O(\frac{n\ln m}{ε^{2}})$. This is significantly better than all known bounds for incremental PageRank. For instance, if we naively recompute the PageRanks as each edge arrives, the simple power iteration method needs $Ω(\frac{m^2}{\ln(1/(1-ε))})$ total time and the Monte Carlo method needs $O(mn/ε)$ total time; both are prohibitively expensive. Furthermore, we also show that we can handle deletions equally efficiently. We then study the computation of the top $k$ personalized PageRanks starting from a seed node, assuming that personalized PageRanks follow a power-law with exponent $α< 1$. We show that if we store $R>q\ln n$ random walks starting from every node for large enough constant $q$ (using the approach outlined for global PageRank), then the expected number of calls made to the distributed social network database is $O(k/(R^{(1-α)/α}))$. We also present experimental results from the social networking site, Twitter, verifying our assumptions and analyses. The overall result is that this algorithm is fast enough for real-time queries over a dynamic social network.

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摘要：

英文摘要：

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