关于占用矩和Bloom过滤器效率
On Occupancy Moments and Bloom Filter Efficiency
摘要：
证明了两个多元委员会分布分别属于Berg阶乘级数分布族和Kemp广义超几何阶乘矩分布族。精确的矩公式，上界和下界，统计参数估计提供了经典的占用和委员会分布。推导出的矩方程用于确定准确的公式的误报率和效率的布隆过滤器-概率数据结构用于解决集成员问题。该研究表明，传统的Bloom过滤器分析高估了最小化误报率所需的哈希函数的数量，并表明Bloom过滤器的效率在哈希函数的数量上是单调的。
英文摘要：
Two multivariate committee distributions are shown to belong to Berg's family of factorial series distributions and Kemp's family of generalized hypergeometric factorial moment distributions. Exact moment formulas, upper and lower bounds, and statistical parameter estimators are provided for the classic occupancy and committee distributions. The derived moment equations are used to determine exact formulas for the false-positive rate and efficiency of Bloom filters -- probabilistic data structures used to solve the set membership problem. This study reveals that the conventional Bloom filter analysis overestimates the number of hash functions required to minimize the false-positive rate, and shows that Bloom filter efficiency is monotonic in the number of hash functions.
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