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".
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.
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) |
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.
Do you enjoy solving problems like these? If so, get in touch with us at [email protected]!
