The Bloom Paradox: When not to Use a Bloom Filter?

Bloom filters and counting Bloom filters (CBFs) are widely used in networking device algorithms. They implement fast set representations to support membership queries with limited error. Unlike Bloom filters, CBFs also support element deletions.

In this talk, we 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. We 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. We show that the Bloom paradox also applies to CBFs, and depends on the product of the hashed counters of each element.