An approximate L/sup 1/-difference algorithm for massive data streams

J. Feigenbaum, Sampath Kannan, M. Strauss, Mahesh Viswanathan
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引用次数: 17

Abstract

We give a space-efficient, one-pass algorithm for approximating the L/sup 1/ difference /spl Sigma//sub i/|a/sub i/-b/sub i/| between two functions, when the function values a/sub i/ and b/sub i/ are given as data streams, and their order is chosen by an adversary. Our main technical innovation is a method of constructing families {V/sub j/} of limited independence random variables that are range summable by which we mean that /spl Sigma//sub j=0//sup c-1/ V/sub j/(s) is computable in time polylog(c), for all seeds s. These random variable families may be of interest outside our current application domain, i.e., massive data streams generated by communication networks. Our L/sup 1/-difference algorithm can be viewed as a "sketching" algorithm, in the sense of (A. Broder et al., 1998), and our algorithm performs better than that of Broder et al., when used to approximate the symmetric difference of two sets with small symmetric difference.
海量数据流的近似L/sup 1/差分算法
当函数值a/下标i/和b/下标i/作为数据流给出时,它们的顺序由对手选择,我们给出了一个节省空间的,一次通过的算法来近似两个函数之间的L/下标1/差分/spl Sigma//下标i/|a/下标i/-b/下标i/|。我们的主要技术创新是一种构造家族{V/sub j/}的有限独立随机变量的方法,这些随机变量是范围可求和的,我们的意思是/spl Sigma//sub j=0//sup c-1/ V/sub j/(s)在时间多元log(c)中是可计算的,对于所有种子s。这些随机变量家族可能在我们当前的应用领域之外感兴趣,即由通信网络生成的大量数据流。从(a . Broder et al., 1998)的意义上讲,我们的L/sup 1/-差分算法可以看作是一种“素描”算法,当用于近似两个对称差分较小的集合的对称差分时,我们的算法比Broder et al.的算法表现得更好。
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