Counting Bloom filter
generalization of Bloom filters that tracks the number of times each hash bucket was touched
A counting Bloom filter (CBF) or spectral Bloom filter is a probabilistic data structure that is used to test whether the number of occurrences of a given element in a sequence exceeds a given threshold. As a generalized form of the Bloom filter, false positive matches are possible, but false negatives are not – in other words, a query returns either "possibly bigger or equal than the threshold" or "definitely smaller than the threshold".
Algorithm description
Most of the parameters are defined same with Bloom filter, such as m, k. m is the number of counters in counting Bloom filter, which is expansion of m bits in Bloom filter. An empty counting Bloom filter is a m counters, all set to 0. Similar to Bloom filter, there must also be k different hash functions defined, each of which maps or hashes some set element to one of the m counter array positions, generating a uniform random distribution. It is also similar that k is a constant, much smaller than m, which is proportional to the number of elements to be added.
The main generalization of Bloom filter is adding an element. To add an element, feed it to each of the k hash functions to get k array positions and increment the counters 1 at all these positions.
To query for an element with a threshold θ (test whether the count number of an element is smaller than θ), feed it to each of the k hash functions to get k counter positions.
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