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In this paper, the authors uncover the Bloom paradox in Bloom filters: sometimes, it is better to disregard the query results of Bloom filters, and in fact not to even query them, thus making them useless. They first analyze conditions under which the Bloom paradox occurs in a Bloom filter, and demonstrate that it depends on the a priori probability that a given element belongs to the represented set. They show that the Bloom paradox also applies to Counting Bloom Filters (CBFs), and depends on the product of the hashed counters of each element. In addition, both for Bloom filters and CBFs, they suggest improved architectures that deal with the Bloom paradox.
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