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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 ...
In computing, the count–min sketch (CM sketch) is a probabilistic data structure that serves as a frequency table of events in a stream of data. It uses hash functions to map events to frequencies, but unlike a hash table uses only sub-linear space , at the expense of overcounting some events due to collisions .
Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed as a function of the size of the input.
Here, complexity refers to the time complexity of performing computations on a multitape Turing machine. [1] See big O notation for an explanation of the notation used. Note: Due to the variety of multiplication algorithms, () below stands in for the complexity of the chosen multiplication algorithm.
The worst-case complexity is the maximum of the complexity over all inputs of size n, and the average-case complexity is the average of the complexity over all inputs of size n (this makes sense, as the number of possible inputs of a given size is finite). Generally, when "complexity" is used without being further specified, this is the worst ...
These algorithms are designed to operate with limited memory, generally logarithmic in the size of the stream and/or in the maximum value in the stream, and may also have limited processing time per item. As a result of these constraints, streaming algorithms often produce approximate answers based on a summary or "sketch" of the data stream.
Generally speaking, elementary and middle school students are best served by scientific calculators; high school students probably need graphing calculators; and professionals who work with ...
Average-case complexity: This is the complexity of solving the problem on an average. This complexity is only defined with respect to a probability distribution over the inputs. For instance, if all inputs of the same size are assumed to be equally likely to appear, the average case complexity can be defined with respect to the uniform ...