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We discuss the problem of counting distinct elements in a stream. A stream isusually considered as a sequence of elements that come one at a time. An exactsolution to the problem requires memory space of the size of the stream. Formany applications this solution is infeasible due to very large streams. Thesolution in that case, is to use a probabilistic data structure (also calledsketch), from which we can estimate with high accuracy the cardinality of thestream. We present a new algorithm, ExtendedHyperLogLog (EHLL), which is basedon the state-of-the-art algorithm, HyperLogLog (HLL). In order to achieve thesame accuracy as HLL, EHLL uses 16% less memory. In recent years, a martingaleapproach has bean developed. In the martingale setting we receive betteraccuracy at the price of not being able to merge sketches. EHLL also works inthe martingale setting. Martingale EHLL achieves the same accuracy asMartingale HLL using 12% less memory.

ExtendedHyperLogLog: Analysis of a new Cardinality Estimator