  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.
