Popular approximate membership query structures such as Bloom filters and cuckoo filters are widely used in databases, security, and networking. These structures represent sets approximately, and support at least two operations - insert and lookup; lookup always returns true on elements inserted into the structure; it also returns true with some probability 0 < ε < 1 on elements not inserted into the structure. These latter elements are called false positives. Compensatory for these false

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... ves, filters can be much smaller than hash tables that represent the same set. However, unlike hash tables, cuckoo filters and Bloom filters must be initialized with the intended number of inserts to be performed, and cannot grow larger - inserts beyond this number fail or significantly increase the false positive probability. This paper presents designs and implementations of filters than can grow without inserts failing and without meaningfully increasing the false positive probability, even if the filters are created with a small initial size. The resulting code is available on GitHub under a permissive open source license.