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The information presented in this paper defines LogLog-Beta. LogLog-Beta is anew algorithm for estimating cardinalities based on LogLog counting. The newalgorithm uses only one formula and needs no additional bias corrections forthe entire range of cardinalities, therefore, it is more efficient and simplerto implement. Our simulations show that the accuracy provided by the newalgorithm is as good as or better than the accuracy provided by either ofHyperLogLog or HyperLogLog++. In addition to LogLog-Beta we also provideanother one-formula estimator for cardinalities based on order statistics, amodification of an algorithm developed by Lumbroso.

LogLog-Beta and More: A New Algorithm for Cardinality Estimation Based on LogLog Counting