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We describe a new cardinality estimation algorithm that is extremelyspace-efficient. It applies one of three novel estimators to the compressedstate of the Flajolet-Martin-85 coupon collection process. In anapples-to-apples empirical comparison against compressed HyperLogLog sketches,the new algorithm simultaneously wins on all three dimensions of thetime/space/accuracy tradeoff. Our prototype uses the zstd compression library,and produces sketches that are smaller than the entropy of HLL, so no possibleimplementation of compressed HLL can match its space efficiency. The paper'stechnical contributions include analyses and simulations of the three newestimators, accurate values for the entropies of FM85 and HLL, and anon-trivial method for estimating a double asymptotic limit via simulation.

Back to the Future: an Even More Nearly Optimal Cardinality Estimation Algorithm