Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New cardinality estimation algorithms for HyperLogLog sketches   This paper presents new methods to estimate the cardinalities of data sets
recorded by HyperLogLog sketches. A theoretically motivated extension to the
original estimator is presented that eliminates the bias for small and large
cardinalities. Based on the maximum likelihood principle a second unbiased
method is derived together with a robust and efficient numerical algorithm to
calculate the estimate. The maximum likelihood approach can also be applied to
more than a single HyperLogLog sketch. In particular, it is shown that it gives
more precise cardinality estimates for union, intersection, or relative
complements of two sets that are both represented by HyperLogLog sketches
compared to the conventional technique using the inclusion-exclusion principle.
All the new methods are demonstrated and verified by extensive simulations.

15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th