An improved version of HyperLogLog for the count-distinct problem, approximating the number of distinct elements in a multiset using 33-50% 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:, Exact, Axiom (8.2 KB), Influx (16.39 KB), ---, ---, ---, 10, 10 (0.0% off), 10 (0.0% off), 50, 50 (0.0% off), 50 (0.0% off), 250, 250 (0.0% off), 250 (0.0% off), 1250, 1249 (0.08% off), 1249 (0.08% off), 6250, 6250 (0.0% off), 6250 (0.0% off), 31250, 31008 (0.7744% off), 31565 (1.0080% off), 156250, 156013 (0.1517% off), 156652 (0.2573% off), 781250, 782364 (0.1426% off), 775988 (0.6735% off), 3906250, 3869332 (0.9451% off), 3889909 (0.4183% off), 10000000, 9952682 (0.4732% off), 9889556 (1.1044% off), ## 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".
An Axiom production.
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