Fig. 2

Cardinality estimation using HyperLogLog for randomly sampled k-mers from microbial genomes. Left: standard deviations of the relative errors of the estimate with precision p ranging from 10 to 18. No systematic biases are apparent, and, as expected, the errors decrease with higher values of p. Up to cardinalities of about 2^p/4, the relative error is near zero. At higher cardinalities, the error boundaries stay near constant. Right: the size of the registers, space requirement, and expected relative error for HyperLogLog cardinality estimates with different values of p. For example, with a precision p = 14, the expected relative error is 0.81%, and the counter only requires 16 KB of space, which is three orders of magnitude less than that of an exact counter (at a cardinality of one million). Up to cardinalities of 2^p/4, KrakenUniq uses a sparse representation of the counter with a higher precision of 25 and an effective relative error rate of about 0.02%