Analysis of Counting Bloom Filters Used for Count Thresholding

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.

Accurate Counting Bloom Filters for Large-Scale Data Processing

Bloom filters are space-efficient randomized data structures for fast membership queries, allowing false positives. Counting Bloom Filters (CBFs) perform the same operations on dynamic sets that can be updated via insertions and deletions. CBFs have been extensively used in MapReduce to accelerate large-scale data processing on large clusters by reducing the volume of datasets. The false positive probability of CBF should be made as low as possible for filtering out more redundant datasets. In this paper, we propose a multilevel optimization approach to building an Accurate Counting Bloom Filter (ACBF) for reducing the false positive probability. ACBF is constructed by partitioning the counter vector into multiple levels. We propose an optimized ACBF by maximizing the first level size, in order to minimize the false positive probability while maintaining the same functionality as CBF. Simulation results show that the optimized ACBF reduces the false positive probability by up to 98.4% at the same memory consumption compared to CBF. We also implement ACBFs in MapReduce to speed up the reduce-side join. Experiments on realistic datasets show that ACBF reduces the false positive probability by 72.3% as well as the map outputs by 33.9% and improves the join execution times by 20% compared to CBF.