An improved version of HyperLogLog for the count-distinct problem, approximating the number of distinct elements in a multiset using 20-50% less space than other usual HyperLogLog implementations.

This work is based on "Better with fewer bits: Improving the performance of cardinality estimation of large data streams - Qingjun Xiao, You Zhou, Shigang Chen".

Implementation

The core differences between this and other implementations are:

• use metro hash instead of xxhash
• sparse representation for lower cardinalities (like HyperLogLog++)
• loglog-beta for dynamic bias correction medium and high cardinalities.
• 4-bit register instead of 5 (HLL) and 6 (HLL++), but most implementations use 1-byte registers out of convenience

In general it borrows a lot from InfluxData's fork of Clark Duvall's HyperLogLog++ implementation, but uses 50% less space.

Results

A direct comparison with the HyperLogLog++ implementation used by InfluxDB yielded the following results:

Note

A big thank you to Prof. Shigang Chen and his team at the University of Florida who are actively conducting research around "Big Network Data".