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Quotient Filter
A quotient filter is a space-efficient probabilistic data structure used to test whether an element is a member of a set (an approximate membership query filter, AMQ). A query will elicit a reply specifying either that the element is definitely not in the set or that the element is probably in the set. The former result is definitive; ''i.e.'', the test does not generate false negatives. But with the latter result there is some probability, ε, of the test returning "element is in the set" when in fact the element is not present in the set (''i.e.'', a false positive). There is a tradeoff between ε, the false positive rate, and storage size; increasing the filter's storage size reduces ε. Other AMQ operations include "insert" and "optionally delete". The more elements are added to the set, the larger the probability of false positives. A typical application for quotient filters, and other AMQ filters, is to serve as a proxy for the keys in a database on disk. As keys are ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probabilistic
Probability is the branch of mathematics concerning numerical descriptions of how likely an Event (probability theory), event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty."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, . The higher the probability of an event, the more likely it is that the event will occur. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any function that can be used to map data of arbitrary size to fixed-size values. The values returned by a hash function are called ''hash values'', ''hash codes'', ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally and storage space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and structured trees, and the often exponential storage requirements of direct access of state spaces of large or variable-length keys. Use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MinHash
In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating how similar two sets are. The scheme was invented by , and initially used in the AltaVista search engine to detect duplicate web pages and eliminate them from search results.. It has also been applied in large-scale clustering problems, such as clustering documents by the similarity of their sets of words.. Jaccard similarity and minimum hash values The Jaccard similarity coefficient is a commonly used indicator of the similarity between two sets. Let be a set and and be subsets of , then the Jaccard index is defined to be the ratio of the number of elements of their intersection and the number of elements of their union: : J(A,B) = . This value is 0 when the two sets are disjoint, 1 when they are equal, and strictly between 0 and 1 otherwise. Two sets are more similar (i.e. have relatively more members in common) wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sorted Array Merge Tree
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Sorted may refer to: * ''Sorted'' (TV series), a BBC television series *"Sorted for E's & Wizz", a 1995 Pulp song * ''Sorted'' (The Drones album), 1999 * ''Sorted'' (DJ? Acucrack album) * ''Sorted'' (film), a 2000 British thriller film *'' Sorted'', a men's magazine *Sorted Food, British YouTube cooking channel and food website See also * Many-sorted logic * Sort (other) Sort may refer to: * Sorting, any process of arranging items in sequence or in sets ** Sorting algorithm, any algorithm for arranging elements in lists ** Sort (Unix), a Unix utility which sorts the lines of a file ** Sort (C++), a function in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bloom Filter
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-free hash coul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quotient Filter States
In arithmetic, a quotient (from lat, quotiens 'how many times', pronounced ) is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division (in the case of Euclidean division), or as a fraction or a ratio (in the case of proper division). For example, when dividing 20 (the ''dividend'') by 3 (the ''divisor''), the ''quotient'' is "6 with a remainder of 2" in the Euclidean division sense, and 6\tfrac in the proper division sense. In the second sense, a quotient is simply the ratio of a dividend to its divisor. Notation The quotient is most frequently encountered as two numbers, or two variables, divided by a horizontal line. The words "dividend" and "divisor" refer to each individual part, while the word "quotient" refers to the whole. \dfrac \quad \begin & \leftarrow \text \\ & \leftarrow \text \end \Biggr \} \leftarrow \text Integer part definition The quo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Donald Knuth
Donald Ervin Knuth ( ; born January 10, 1938) is an American computer scientist, mathematician, and professor emeritus at Stanford University. He is the 1974 recipient of the ACM Turing Award, informally considered the Nobel Prize of computer science. Knuth has been called the "father of the analysis of algorithms". He is the author of the multi-volume work ''The Art of Computer Programming'' and contributed to the development of the rigorous analysis of the computational complexity of algorithms and systematized formal mathematical techniques for it. In the process, he also popularized the asymptotic notation. In addition to fundamental contributions in several branches of theoretical computer science, Knuth is the creator of the TeX computer typesetting system, the related METAFONT font definition language and rendering system, and the Computer Modern family of typefaces. As a writer and scholar, Knuth created the WEB and CWEB computer programming systems designed to encou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Model Checking
In computer science, model checking or property checking is a method for checking whether a finite-state model of a system meets a given specification (also known as correctness). This is typically associated with hardware or software systems, where the specification contains liveness requirements (such as avoidance of livelock) as well as safety requirements (such as avoidance of states representing a system crash). In order to solve such a problem algorithmically, both the model of the system and its specification are formulated in some precise mathematical language. To this end, the problem is formulated as a task in logic, namely to check whether a structure satisfies a given logical formula. This general concept applies to many kinds of logic and many kinds of structures. A simple model-checking problem consists of verifying whether a formula in the propositional logic is satisfied by a given structure. Overview Property checking is used for verification when two desc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or 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 databases commonly use B-tree indexes for data retrieval, while compiler implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such as large databases and internet indexing services. Usually, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Table
In computing, a hash table, also known as hash map, is a data structure that implements an associative array or dictionary. It is an abstract data type that maps keys to values. A hash table uses a hash function to compute an ''index'', also called a ''hash code'', into an array of ''buckets'' or ''slots'', from which the desired value can be found. During lookup, the key is hashed and the resulting hash indicates where the corresponding value is stored. Ideally, the hash function will assign each key to a unique bucket, but most hash table designs employ an imperfect hash function, which might cause hash ''collisions'' where the hash function generates the same index for more than one key. Such collisions are typically accommodated in some way. In a well-dimensioned hash table, the average time complexity for each lookup is independent of the number of elements stored in the table. Many hash table designs also allow arbitrary insertions and deletions of key–value pairs, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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