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Popular approximate membership query structures such as Bloom filters andcuckoo filters are widely used in databases, security, and networking. Thesestructures represent sets approximately, and support at least two operations -insert and lookup; lookup always returns true on elements inserted into thestructure; it also returns true with some probability $0 < \varepsilon < 1$ onelements not inserted into the structure. These latter elements are calledfalse positives. Compensatory for these false positives, filters can be muchsmaller than hash tables that represent the same set. However, unlike hashtables, cuckoo filters and Bloom filters must be initialized with the intendednumber of inserts to be performed, and cannot grow larger - inserts beyond thisnumber fail or significantly increase the false positive probability. Thispaper presents designs and implementations of filters than can grow withoutinserts failing and without meaningfully increasing the false positiveprobability, even if the filters are created with a small initial size. Theresulting code is available on GitHub under a permissive open source license.

Stretching Your Data With Taffy Filters