HyperLogLog 
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:
| 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".
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