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The HyperLogLog has three main operations: add to add a new element to the set, count to obtain the cardinality of the set and merge to obtain the union of two sets. Some derived operations can be computed using the inclusion–exclusion principle like the cardinality of the intersection or the cardinality of the difference between two HyperLogLogs combining the merge and count operations.
In computer science, the iterated logarithm of , written log * (usually read " log star "), is the number of times the logarithm function must be iteratively applied before the result is less than or equal to . [1] The simplest formal definition is the result of this recurrence relation: In computer science, lg* is often used to indicate the ...
Because log(x) is the sum of the terms of the form log(1 + 2 −k) corresponding to those k for which the factor 1 + 2 −k was included in the product P, log(x) may be computed by simple addition, using a table of log(1 + 2 −k) for all k. Any base may be used for the logarithm table. [53]
In science and engineering, a log–log graph or log–log plot is a two-dimensional graph of numerical data that uses logarithmic scales on both the horizontal and vertical axes. Power functions – relationships of the form – appear as straight lines in a log–log graph, with the exponent corresponding to the slope, and the coefficient ...
Timsort is a stable sorting algorithm (order of elements with same key is kept) and strives to perform balanced merges (a merge thus merges runs of similar sizes). In order to achieve sorting stability, only consecutive runs are merged. Between two non-consecutive runs, there can be an element with the same key inside the runs.
O(n)[1] In computer science, a disjoint-set data structure, also called a union–find data structure or merge–find set, is a data structure that stores a collection of disjoint (non-overlapping) sets. Equivalently, it stores a partition of a set into disjoint subsets. It provides operations for adding new sets, merging sets (replacing them ...
Common logarithm. A graph of the common logarithm of numbers from 0.1 to 100. In mathematics, the common logarithm is the logarithm with base 10. [1] It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered its use, as well as ...
The law of iterated logarithms operates "in between" the law of large numbers and the central limit theorem.There are two versions of the law of large numbers — the weak and the strong — and they both state that the sums S n, scaled by n −1, converge to zero, respectively in probability and almost surely: