Smaller and More Flexible Cuckoo Filters

Abstract

Cuckoo filters are space-efficient approximate set membership data structures with a controllable false positive rate (FPR) and zero false negatives, similar to Bloom filters. In contrast to Bloom filters, Cuckoo filters store multi-bit fingerprints of keys in a hash table using variants of Cuckoo hashing, allowing each fingerprint to be stored at a small number of possible locations. Existing Cuckoo filters use fingerprints of $(k+3)$ bits per key and an additional space overhead factor of at least $1.05$ to achieve an FPR of $2^{-k}$. For $k=10$, this amounts to $1.365\, kn$ bits to store $n$ keys, which is better than $1.443\, kn$ bits for Bloom filters. The $+3$ for the fingerprint size is required to balance out the multiplied FPR caused by looking for the fingerprint at several locations. In the original Cuckoo filter, the number of hash table buckets is restricted to a power of 2, which may lead to much larger space overheads, up to $2.1\, (1+3/k)\, kn$ bits. We present two improvements of Cuckoo filters. First, we remove the restriction that the number of buckets must be a power of 2 by using a different placement strategy. Second, we reduce the space overhead factor of Cuckoo filters to $1.06 \, (1+2/k)$ by using overlapping windows instead of disjoint buckets to maintain the load threshold of the hash table, while reducing the number of alternative slots where any fingerprint may be found. A detailed evaluation demonstrates that the alternative memory layout based on overlapping windows decreases the size of Cuckoo filters not only in theory, but also in practice. A comparison with other state-of-the art filter types, Prefix filters and Vector Quotient filters (VQFs), shows that the reduced space overhead makes windowed Cuckoo filters the smallest filters supporting online insertions, with similarly fast queries, but longer insertion times.