A cuckoo filter is a space-efficient probabilistic data structure used to test set membership with low false positives and support for element deletion and counting. It works by hashing elements to multiple buckets, each holding a small, fixed-size fingerprint of the element. When testing for membership, the filter checks the corresponding buckets for the presence of the element's fingerprint. False positives are possible due to hash collisions, but false negatives are not.

Compared to a bloom filter, cuckoo filters can achieve lower space overhead and allow for element deletion and counting. However, they require more memory per element and their performance can degrade when the load factor exceeds a certain threshold. Cuckoo filters use a -way set-associative hash table based on cuckoo hashing to store fingerprints and enable item relocation based only on fingerprints.

Choosing between a bloom filter and a cuckoo filter depends on the specific requirements of the application, such as the desired false positive rate, the need for element deletion and counting, and the available memory budget.
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