SetSketch: Filling the Gap between MinHash and HyperLogLog Otmar Ertl Dynatrace Research Linz, Austria
[email protected] ABSTRACT Commutativity: The order of insert operations should not be rele- MinHash and HyperLogLog are sketching algorithms that have vant for the fnal state. If the processing order cannot be guaranteed, become indispensable for set summaries in big data applications. commutativity is needed to get reproducible results. Many data While HyperLogLog allows counting diferent elements with very structures are not commutative [13, 32, 65]. little space, MinHash is suitable for the fast comparison of sets as it Mergeability: In large-scale applications with distributed data allows estimating the Jaccard similarity and other joint quantities. sources it is essential that the data structure supports the union set This work presents a new data structure called SetSketch that is operation. It allows combining data sketches resulting from partial able to continuously fll the gap between both use cases. Its commu- data streams to get an overall result. Ideally, the union operation tative and idempotent insert operation and its mergeable state make is idempotent, associative, and commutative to get reproducible it suitable for distributed environments. Fast, robust, and easy-to- results. Some data structures trade mergeability for better space implement estimators for cardinality and joint quantities, as well efciency [11, 13, 65]. as the ability to use SetSketch for similarity search, enable versatile Space efciency: A small memory footprint is the key purpose of applications. The presented joint estimator can also be applied to data sketches. They generally allow to trade space for estimation other data structures such as MinHash, HyperLogLog, or Hyper- accuracy, since variance is typically inversely proportional to the MinHash, where it even performs better than the corresponding sketch size.