可逆Bloom过滤器部分提取的失效概率分析
Failure Probability Analysis for Partial Extraction from Invertible Bloom Filters
摘要：
可逆布隆过滤器（IBF）是一种数据结构，它使用一组小的哈希函数。IBF允许有效的插入，并且以高概率允许有效的数据提取。然而，提取的成功概率取决于IBF的存储开销和存储的数据量。在需要提取IBF中存储的数据的应用程序（例如集合协调）中，通过仅恢复部分存储数据，提取可能仅部分成功。在这项工作中，成功的概率从IBF的数据的部分提取进行了分析。结果表明，部分提取可能是有用的应用程序，如设置和解。特别是，它允许通过使用IBF进行集合协调，其中存储开销太小而不允许完全提取。给出了迭代集合协调协议中轮数的一个上界。数值结果是解析推导的，并通过计算机模拟证实。
英文摘要：
Invertible Bloom Filter (IBF) is a data structure, which employs a small set of hash functions. An IBF allows for an efficient insertion and, with high probability, for an efficient extraction of the data. However, the success probability of the extraction depends on the storage overhead of an IBF and the amount of the data stored. In an application, such as set reconciliation, where there is a need to extract data stored in the IBF, the extraction might succeed only partially, by recovering only part of the stored data. In this work, the probability of success for a partial extraction of data from an IBF is analyzed. It is shown that partial extraction could be useful in applications, such as set reconciliation. In particular, it allows for set reconciliation by using the IBF, where the storage overhead is too small to allow full extraction. An upper bound on the number of rounds in an iterative set reconciliation protocol is presented. The numerical results are derived analytically, and confirmed by the computer simulations.
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