SetSketch: Filling the Gap between MinHash and HyperLogLog

MinHash and HyperLogLog are sketching algorithms that have become indispensable for set summaries in big data applications. While HyperLogLog allows counting different elements with very little space, MinHash is suitable for the fast comparison of sets as it allows estimating the Jaccard similarity and other joint quantities. This work presents a new data structure called SetSketch that is able to continuously fill the gap between both use cases. Its commutative and idempotent insert operation and its mergeable state make it suitable for distributed environments. Robust and easy-to-implement estimators for cardinality and joint quantities, as well as the ability to use SetSketch for similarity search, enable versatile applications. The developed methods can also be used for HyperLogLog sketches and allow estimation of joint quantities such as the intersection size with a smaller error compared to the common estimation approach based on the inclusion-exclusion principle.