A cuckoo filter is a probabilistic data structure used to test for the presence of an element in a set. It is similar to a Bloom filter, but is more space-efficient and allows for deletions.

The way a cuckoo filter works is by hashing the elements of a set into a number of buckets, each of which contains a small number of elements. Each bucket has a fingerprint, which is a small hash of the elements stored in the bucket. When checking for the presence of an element in the filter, the element is hashed and its fingerprint is checked against the fingerprints of the buckets it could be stored in. If the fingerprint is found in one of those buckets, the element is considered to be present in the filter.

If the element's fingerprint is not found in any of the candidate buckets, the element can be added to one of them by swapping it with the existing element in the bucket, and repeating the process until a vacant bucket is found. If the filter is full or the swapping process exceeds a certain number of iterations, the filter is considered to be at capacity and the element is not added.

Cuckoo filters are advantageous over Bloom filters when the false positive rate needs to be controlled and deletions from the filter are required. Unlike Bloom filters, cuckoo filters can also support deletions, which means it's possible to remove an element from the set without having to rebuild the entire filter. Cuckoo filters also require less space than Bloom filters and have better performance for larger sets, making them a more efficient choice in certain cases.
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