用浮点计数器近似计数
Approximate counting with a floating-point counter
摘要：
在当代应用中，内存成为一个限制因素，例如Webgraph和分子序列分析，当许多对象需要同时计数时。Robert Morris [Communications of the ACM，21：840- 842，1978]提出了一种非常节省空间的近似计数的概率技术。基本思想是以概率$2^{-X}$递增包含值$X$的计数器。因此，计数器包含存储在$\lg\lg n$位中的$n$概率更新之后的$\lg n$的近似值。在这里，我们重新审视莫里斯的原始想法，并介绍一个二进制浮点计数器，它使用一个$d$位有效数结合一个二进制指数。计数器产生一个简单的公式，用于$n$的无偏估计，标准偏差约为$0.6\cdot n2^{-d/2}$，并使用$d+\lg\lg n$位。我们分析了浮点计数器的性能，适用于任何概率计数器的一般框架，并推导出实用的公式来评估其准确性。
英文摘要：
Memory becomes a limiting factor in contemporary applications, such as analyses of the Webgraph and molecular sequences, when many objects need to be counted simultaneously. Robert Morris [Communications of the ACM, 21:840--842, 1978] proposed a probabilistic technique for approximate counting that is extremely space-efficient. The basic idea is to increment a counter containing the value $X$ with probability $2^{-X}$. As a result, the counter contains an approximation of $\lg n$ after $n$ probabilistic updates stored in $\lg\lg n$ bits. Here we revisit the original idea of Morris, and introduce a binary floating-point counter that uses a $d$-bit significand in conjunction with a binary exponent. The counter yields a simple formula for an unbiased estimation of $n$ with a standard deviation of about $0.6\cdot n2^{-d/2}$, and uses $d+\lg\lg n$ bits. We analyze the floating-point counter's performance in a general framework that applies to any probabilistic counter, and derive practical formulas to assess its accuracy.
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