HyperLogLog: the analysis of a near-optimal cardinality estimation algorithm

Abstract

This extended abstract describes and analyses a near-optimal probabilistic algorithm, HYPERLOGLOG, dedicated to estimating the number of \emphdistinct elements (the cardinality) of very large data ensembles. Using an auxiliary memory of m units (typically, "short bytes''), HYPERLOGLOG performs a single pass over the data and produces an estimate of the cardinality such that the relative accuracy (the standard error) is typically about $1.04/\sqrt{m}$. This improves on the best previously known cardinality estimator, LOGLOG, whose accuracy can be matched by consuming only 64% of the original memory. For instance, the new algorithm makes it possible to estimate cardinalities well beyond $10^9$ with a typical accuracy of 2% while using a memory of only 1.5 kilobytes. The algorithm parallelizes optimally and adapts to the sliding window model.

Keywords

• cardinality estimation
• probabilistic algorithm
• [info.info-ds] computer science [cs]/data structures and algorithms [cs.ds]
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]
• [info.info-cg] computer science [cs]/computational geometry [cs.cg]