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The count–min sketch was invented in 2003 by Graham Cormode and S. Muthu Muthukrishnan [1] and described by them in a 2005 paper. [2] Count–min sketch is an alternative to count sketch and AMS sketch and can be considered an implementation of a counting Bloom filter (Fan et al., 1998 [3]) or multistage-filter. [1]
If all are greater or equal to θ even though the count is smaller than θ, this circumstance is defined as false positive. This also should be minimized like Bloom filter. About hashing problem and advantages, see Bloom filter. A counting Bloom filter is essentially the same data structure as count–min sketches, but are used differently.
Count sketch is a type of dimensionality reduction that is particularly efficient in statistics, machine learning and algorithms. [1] [2] It was invented by Moses Charikar, Kevin Chen and Martin Farach-Colton [3] in an effort to speed up the AMS Sketch by Alon, Matias and Szegedy for approximating the frequency moments of streams [4] (these calculations require counting of the number of ...
Count–min sketch – Probabilistic data structure in computer science; Feature hashing – Vectorizing features using a hash function; MinHash – Data mining technique; Quotient filter; Skip list – Probabilistic data structure; Bloom filters in bioinformatics; Cuckoo filter – Data structure for approximate set membership
It is not possible for a streaming algorithm with memory sublinear in both and to solve selection queries exactly for dynamic data, but the count–min sketch can be used to solve selection queries approximately, by finding a value whose position in the ordering of the elements (if it were added to them) would be within steps of , for a sketch ...
There are other estimation techniques other than min/max sketches. The first paper on count-distinct estimation [7] describes the Flajolet–Martin algorithm, a bit pattern sketch. In this case, the elements are hashed into a bit vector and the sketch holds the logical OR of all hashed values.
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.
Though streaming algorithms had already been studied by Munro and Paterson [1] as early as 1978, as well as Philippe Flajolet and G. Nigel Martin in 1982/83, [2] the field of streaming algorithms was first formalized and popularized in a 1996 paper by Noga Alon, Yossi Matias, and Mario Szegedy. [3]