A bloom filter is an extremely useful tool applicable to various fields of electronics and computers; it enables highly efficient search of extremely large data sets with no false negatives but a possibly small number of false positives. A counting bloom filter is a variant of a bloom filter that is typically used to permit deletions as well as additions of elements to a target data set. However, it is also sometimes useful to use a counting bloom filter as an approximate counting mechanism that can be used, for example, to determine when a specific web page has been referenced more than a specific number of times or when a memory address is a “hot” address. This paper derives, for the first time, highly accurate approximate false positive probabilities and optimal numbers of hash functions for counting bloom filters used in count thresholding applications. The analysis is confirmed by comparisons to existing theoretical results, which show an error, with respect to exact analysis, of less than 0.48% for typical parameter values.
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