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In computer science, the count-distinct problem [1] (also known in applied mathematics as the cardinality estimation problem) is the problem of finding the number of distinct elements in a data stream with repeated elements. This is a well-known problem with numerous applications.
The Flajolet–Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem).
The effect of Yates's correction is to prevent overestimation of statistical significance for small data. This formula is chiefly used when at least one cell of the table has an expected count smaller than 5. = = The following is Yates's corrected version of Pearson's chi-squared statistics:
If the maximum number of leading zeros observed is n, an estimate for the number of distinct elements in the set is 2 n. [1] In the HyperLogLog algorithm, a hash function is applied to each element in the original multiset to obtain a multiset of uniformly distributed random numbers with the same cardinality as the original multiset. The ...
Elements that occur more than / times in a multiset of size may be found by a comparison-based algorithm, the Misra–Gries heavy hitters algorithm, in time (). The element distinctness problem is a special case of this problem where k = n {\displaystyle k=n} .
In the field of streaming algorithms, Misra–Gries summaries are used to solve the frequent elements problem in the data stream model.That is, given a long stream of input that can only be examined once (and in some arbitrary order), the Misra-Gries algorithm [1] can be used to compute which (if any) value makes up a majority of the stream, or more generally, the set of items that constitute ...
Here a first-level hash function g is also used to map elements onto a range of r integers. An element x ∈ S is stored in the Bucket B g(x). [4] Then, in descending order of size, each bucket's elements are hashed by a hash function of a sequence of independent fully random hash functions (Φ 1, Φ 2, Φ 3, ...), starting with Φ 1. If the ...
Thus, a problem on elements is reduced to two recursive problems on / elements (to find the pivot) and at most / elements (after the pivot is used). The total size of these two recursive subproblems is at most 9 n / 10 {\displaystyle 9n/10} , allowing the total time to be analyzed as a geometric series adding to O ( n ) {\displaystyle O(n)} .
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