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HyperLogLog: counting distinct items with a small sketch

Contribution grade

Approximate distinct counting · Approximate distinct counting

Reference score110,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

HyperLogLog estimates the number of distinct stream items by combining per-bucket bit-pattern registers through a normalized harmonic mean, reducing variance while keeping a small mergeable state.

Scientific scope

HyperLogLog estimates the number of distinct stream items by combining per-bucket bit-pattern registers through a normalized harmonic mean, reducing variance while keeping a small mergeable state. The estimator assumes a sufficiently uniform, shared hash function and fixed register configuration. Its approximately 1.04/sqrt(m) relative standard error is an asymptotic distributional statement, not a deterministic error bound for every stream. The analysis orders the large-cardinality and large-register limits. Small-range and hash-collision corrections have their own conditions. Registerwise maximum merges compatible streams but does not support deletion. The original extended abstract sketches some analytic steps. Later HyperLogLog++ improvements are separate. WRS has not reconstructed the full probability proof or replayed the published simulations.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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