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The Story of HyperLogLog: How Flajolet Processed Streams with Coin Flips
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This article is a historical introduction to data streaming algorithms that was written as a companion piece to the talk "How Philippe Flipped Coins to Count Data", given on December 16th, 2011, in the context of the conference in honor of "Philippe Flajolet and Analytic Combinatorics." The narrative was pieced together through conversations with Philippe Flajolet during my Ph.D. thesis under his supervision, as well as several conversations with collaborators after his death. In particular, I am deeply indebted to Nigel Martin for his archival records. This article is intended to serve as an introductory text presenting Flajolet's data streaming articles in a projected set of complete works.
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HyperLogLog for probabilists
HyperLogLog's raw estimator satisfies P(m²Z_N ≤ μN) ≤ exp(−m(1/μ − 1 + log μ)) for every N ≥ 1, plus a right-tail bound with an explicit correction term.
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