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Cuckoo Filter
A cuckoo filter is a space-efficient probabilistic data structure that is used to test whether an element is a member of a set, like a Bloom filter does. False positive matches are possible, but false negatives are not – in other words, a query returns either "possibly in set" or "definitely not in set". A cuckoo filter can also delete existing items, which is not supported by Bloom filters. In addition, for applications that store many items and target moderately low false positive rates, cuckoo filters can achieve lower space overhead than space-optimized Bloom filters. Cuckoo filters were first described in 2014. Algorithm description A cuckoo filter uses a hash table based on cuckoo hashing to store the fingerprints of items. The data structure is broken into buckets of some size b. To insert the fingerprint of an item x, one first computes two potential buckets h_1(x) and h_2(x) where x could go. These buckets are calculated using the formula :h_1(x)=\text(x) :h_2(x)=h_1(x ...
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Probabilistic
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ...
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Data Structure
In computer science, a data structure is a data organization and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the Function (computer programming), functions or Operator (computer programming), operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, Relational database, relational databases commonly use B-tree indexes for data retrieval, while compiler Implementation, implementations usually use hash tables to look up Identifier (computer languages), identifiers. Data s ...
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Element (mathematics)
In mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ..., an element (or member) of a set is any one of the distinct objects that belong to that set. For example, given a set called containing the first four positive integers (A = \), one could say that "3 is an element of ", expressed notationally as 3 \in A . Sets Writing A = \ means that the elements of the set are the numbers 1, 2, 3 and 4. Sets of elements of , for example \, are subsets of . Sets can themselves be elements. For example, consider the set B = \. The elements of are ''not'' 1, 2, 3, and 4. Rather, there are only three elements of , namely the numbers 1 and 2, and the set \. The elements of a set can be anything. For example the elements of the set C = \ are the color red, the number 12, ...
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Set (computer Science)
In computer science, a set is an abstract data type that can store unique values, without any particular sequence, order. It is a computer implementation of the mathematics, mathematical concept of a finite set. Unlike most other collection (abstract data type), collection types, rather than retrieving a specific element from a set, one typically tests a value for membership in a set. Some set data structures are designed for static or frozen sets that do not change after they are constructed. Static sets allow only query operations on their elements — such as checking whether a given value is in the set, or enumerating the values in some arbitrary order. Other variants, called dynamic or mutable sets, allow also the insertion and deletion of elements from the set. A multiset is a special kind of set in which an element can appear multiple times in the set. Type theory In type theory, sets are generally identified with their indicator function (characteristic function): accord ...
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Bloom Filter
In computing, a Bloom filter is a space-efficient probabilistic data structure, conceived by Burton Howard Bloom in 1970, that is used to test whether an element is a member of a set. False positive matches are possible, but false negatives are not – in other words, a query returns either "possibly in set" or "definitely not in set". Elements can be added to the set, but not removed (though this can be addressed with the counting Bloom filter variant); the more items added, the larger the probability of false positives. Bloom proposed the technique for applications where the amount of source data would require an impractically large amount of memory if "conventional" error-free hashing techniques were applied. He gave the example of a hyphenation algorithm for a dictionary of 500,000 words, out of which 90% follow simple hyphenation rules, but the remaining 10% require expensive disk accesses to retrieve specific hyphenation patterns. With sufficient core memory, an error- ...
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Type I And Type II Errors
Type I error, or a false positive, is the erroneous rejection of a true null hypothesis in statistical hypothesis testing. A type II error, or a false negative, is the erroneous failure in bringing about appropriate rejection of a false null hypothesis. Type I errors can be thought of as errors of commission, in which the status quo is erroneously rejected in favour of new, misleading information. Type II errors can be thought of as errors of omission, in which a misleading status quo is allowed to remain due to failures in identifying it as such. For example, if the assumption that people are ''innocent until proven guilty'' were taken as a null hypothesis, then proving an innocent person as guilty would constitute a Type I error, while failing to prove a guilty person as guilty would constitute a Type II error. If the null hypothesis were inverted, such that people were by default presumed to be ''guilty until proven innocent'', then proving a guilty person's innocence would ...
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Cuckoo Hashing
Cuckoo hashing is a scheme in computer programming for resolving hash collisions of values of hash functions in a table, with worst-case constant lookup time. The name derives from the behavior of some species of cuckoo, where the cuckoo chick pushes the other eggs or young out of the nest when it hatches in a variation of the behavior referred to as brood parasitism; analogously, inserting a new key into a cuckoo hashing table may push an older key to a different location in the table. History Cuckoo hashing was first described by Rasmus Pagh and Flemming Friche Rodler in a 2001 conference paper. The paper was awarded the European Symposium on Algorithms Test-of-Time award in 2020. Operations Cuckoo hashing is a form of open addressing in which each non-empty cell of a hash table contains a key or key–value pair. A hash function is used to determine the location for each key, and its presence in the table (or the value associated with it) can be found by examining that c ...
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Fingerprint (computing)
In computer science, a fingerprinting algorithm is a procedure that maps an arbitrarily large data item (remove, as a computer file) to a much shorter bit string, its ''fingerprint'', that uniquely identifies the original data for all practical purposes just as human fingerprints uniquely identify people for practical purposes. This fingerprint may be used for data deduplication purposes. This is also referred to as ''file fingerprinting'', ''data fingerprinting'', or ''structured data fingerprinting''. Fingerprints are typically used to avoid the comparison and transmission of bulky data. For instance, a remove, web browser or proxy server can efficiently check whether a remote, by fetching only its fingerprint and comparing it with that of the previously fetched copy. Fingerprint functions may be seen as high-performance hash functions used to uniquely identify substantial blocks of data where cryptographic functions may be. Special algorithms exist for audio and video fingerpr ...
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Probabilistic Data Structures
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur."Kendall's Advanced Theory of Statistics, Volume 1: Distribution Theory", Alan Stuart and Keith Ord, 6th ed., (2009), .William Feller, ''An Introduction to Probability Theory and Its Applications'', vol. 1, 3rd ed., (1968), Wiley, . This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin. Since the coin is fair, the two outcomes ("heads" and "tails") are both equally probable; the probability of "heads" equals the probability of "tails"; and since no other outcomes are possible, the probability of either "heads" or "tails" is 1/2 (which could also be written as 0.5 or 50%). These concepts have been given an axiomatic mathematical formaliza ...
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Lossy Compression Algorithms
In information technology, lossy compression or irreversible compression is the class of data compression methods that uses inexact approximations and partial data discarding to represent the content. These techniques are used to reduce data size for storing, handling, and transmitting content. Higher degrees of approximation create coarser images as more details are removed. This is opposed to lossless data compression (reversible data compression) which does not degrade the data. The amount of data reduction possible using lossy compression is much higher than using lossless techniques. Well-designed lossy compression technology often reduces file sizes significantly before degradation is noticed by the end-user. Even when noticeable by the user, further data reduction may be desirable (e.g., for real-time communication or to reduce transmission times or storage needs). The most widely used lossy compression algorithm is the discrete cosine transform (DCT), first published by N ...
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