HyperLogLogLog: Cardinality Estimation With One Log More

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We present HyperLogLogLog, a practical compression of the HyperLogLog sketch that compresses the sketch from O(mogog n) bits down to m log2log2log2 m + O(m+loglog n) bits for estimating the number of distinct elements∼n using m∼registers. The algorithm works as a drop-in replacement that preserves all estimation properties of the HyperLogLog sketch, it is possible to convert back and forth between the compressed and uncompressed representations, and the compressed sketch maintains mergeability in the compressed domain. The compressed sketch can be updated in amortized constant time, assuming n is sufficiently larger than m. We provide a C++ implementation of the sketch, and show by experimental evaluation against well-known implementations by Google and Apache that our implementation provides small sketches while maintaining competitive update and merge times. Concretely, we observed approximately a 40% reduction in the sketch size. Furthermore, we obtain as a corollary a theoretical algorithm that compresses the sketch down to mlog2log2log2log2 m+O(mlogloglog m/loglog m+loglog n) bits.

TitelKDD 2022 - Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining
ForlagAssociation for Computing Machinery, Inc.
ISBN (Elektronisk)9781450393850
StatusUdgivet - 2022
Begivenhed28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2022 - Washington, USA
Varighed: 14 aug. 202218 aug. 2022


Konference28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, KDD 2022

Bibliografisk note

Funding Information:
We thank Martin Aumüller for constructive discussions. This work was supported by VILLUM Foundation grant 16582.

Publisher Copyright:
© 2022 ACM.

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