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Universal Hashing
In mathematics and computing, universal hashing (in a randomized algorithm or data structure) refers to selecting a hash function at random from a family of hash functions with a certain mathematical property (see definition below). This guarantees a low number of collisions in expectation, even if the data is chosen by an adversary. Many universal families are known (for hashing integers, vectors, strings), and their evaluation is often very efficient. Universal hashing has numerous uses in computer science, for example in implementations of hash tables, randomized algorithms, and cryptography. Introduction Assume we want to map keys from some universe U into m bins (labelled = \). The algorithm will have to handle some data set S \subseteq U of , S, =n keys, which is not known in advance. Usually, the goal of hashing is to obtain a low number of collisions (keys from S that land in the same bin). A deterministic hash function cannot offer any guarantee in an adversarial sett ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Distribution
In probability theory and statistics, the geometric distribution is either one of two discrete probability distributions: * The probability distribution of the number ''X'' of Bernoulli trials needed to get one success, supported on the set \; * The probability distribution of the number ''Y'' = ''X'' − 1 of failures before the first success, supported on the set \. Which of these is called the geometric distribution is a matter of convention and convenience. These two different geometric distributions should not be confused with each other. Often, the name ''shifted'' geometric distribution is adopted for the former one (distribution of the number ''X''); however, to avoid ambiguity, it is considered wise to indicate which is intended, by mentioning the support explicitly. The geometric distribution gives the probability that the first occurrence of success requires ''k'' independent trials, each with success probability ''p''. If the probability of suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Masking
In computer science, a mask or bitmask is data that is used for bitwise operations, particularly in a bit field. Using a mask, multiple bits in a byte, nibble, word, etc. can be set either on or off, or inverted from on to off (or vice versa) in a single bitwise operation. An additional use of masking involves predication in vector processing, where the bitmask is used to select which element operations in the vector are to be executed (mask bit is enabled) and which are not (mask bit is clear). Common bitmask functions Masking bits to 1 To turn certain bits on, the bitwise OR operation can be used, following the principle that Y OR 1 = 1 and Y OR 0 = Y. Therefore, to make sure a bit is on, OR can be used with a 1. To leave a bit unchanged, OR is used with a 0. Example: Masking ''on'' the higher nibble (bits 4, 5, 6, 7) while leaving the lower nibble (bits 0, 1, 2, 3) unchanged. 10010101 10100101 OR 11110000 11110000 = 11110101 11110101 Masking bits to 0 Mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mersenne Prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th century. If is a composite number then so is . Therefore, an equivalent definition of the Mersenne primes is that they are the prime numbers of the form for some prime . The exponents which give Mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31, ... and the resulting Mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, ... . Numbers of the form without the primality requirement may be called Mersenne numbers. Sometimes, however, Mersenne numbers are defined to have the additional requirement that be prime. The smallest composite Mersenne number with prime exponent ''n'' is . Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buzhash
A rolling hash (also known as recursive hashing or rolling checksum) is a hash function where the input is hashed in a window that moves through the input. A few hash functions allow a rolling hash to be computed very quickly—the new hash value is rapidly calculated given only the old hash value, the old value removed from the window, and the new value added to the window—similar to the way a moving average function can be computed much more quickly than other low-pass filters. One of the main applications is the Rabin–Karp string search algorithm, which uses the rolling hash described below. Another popular application is the rsync program, which uses a checksum based on Mark Adler's adler-32 as its rolling hash. Low Bandwidth Network Filesystem (LBFS) uses a Rabin fingerprint as its rolling hash. FastCDC (Fast Content-Defined Chunking) uses a compute-efficient Gear fingerprint as its rolling hash. At best, rolling hash values are pairwise independentDaniel Lemire, Owen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rabin Fingerprint
The Rabin fingerprinting scheme is a method for implementing fingerprints using polynomials over a finite field. It was proposed by Michael O. Rabin. Scheme Given an ''n''-bit message ''m''0,...,''m''n-1, we view it as a polynomial of degree ''n''-1 over the finite field GF(2). : f(x) = m_0 + m_1 x + \ldots + m_ x^ We then pick a random irreducible polynomial of degree ''k'' over GF(2), and we define the fingerprint of the message ''m'' to be the remainder r(x) after division of f(x) by p(x) over GF(2) which can be viewed as a polynomial of degree or as a ''k''-bit number. Applications Many implementations of the Rabin–Karp algorithm internally use Rabin fingerprints. The ''Low Bandwidth Network Filesystem'' (LBFS) from MIT uses Rabin fingerprints to implement variable size shift-resistant blocks.Athicha Muthitacharoen, Benjie Chen, and David Mazières"A Low-bandwidth Network File System"/ref> The basic idea is that the filesystem computes the cryptographic hash of each blo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dennis Ritchie
Dennis MacAlistair Ritchie (September 9, 1941 – October 12, 2011) was an American computer scientist. He is most well-known for creating the C programming language and, with long-time colleague Ken Thompson, the Unix operating system and B programming language. Ritchie and Thompson were awarded the Turing Award from the ACM in 1983, the Hamming Medal from the IEEE in 1990 and the National Medal of Technology from President Bill Clinton in 1999. Ritchie was the head of Lucent Technologies System Software Research Department when he retired in 2007. He was the "R" in K&R C, and commonly known by his username dmr. Personal life and career Dennis Ritchie was born in Bronxville, New York. His father was Alistair E. Ritchie, a longtime Bell Labs scientist and co-author of ''The Design of Switching Circuits'' on switching circuit theory. As a child, Dennis moved with his family to Summit, New Jersey, where he graduated from Summit High School. He graduated from Harva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brian Kernighan
Brian Wilson Kernighan (; born 1942) is a Canadian computer scientist. He worked at Bell Labs and contributed to the development of Unix alongside Unix creators Ken Thompson and Dennis Ritchie. Kernighan's name became widely known through co-authorship of the first book on the C programming language (''The C Programming Language'') with Dennis Ritchie. Kernighan affirmed that he had no part in the design of the C language ("it's entirely Dennis Ritchie's work"). He authored many Unix programs, including ditroff. Kernighan is coauthor of the AWK and AMPL programming languages. The "K" of K&R C and of AWK both stand for "Kernighan". In collaboration with Shen Lin he devised well-known heuristics for two NP-complete optimization problems: graph partitioning and the travelling salesman problem. In a display of authorial equity, the former is usually called the Kernighan–Lin algorithm, while the latter is known as the Lin–Kernighan heuristic. Kernighan has been a P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel J
Daniel is a masculine given name and a surname of Hebrew origin. It means "God is my judge"Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 68. (cf. Gabriel—"God is my strength"), and derives from two early biblical figures, primary among them Daniel from the Book of Daniel. It is a common given name for males, and is also used as a surname. It is also the basis for various derived given names and surnames. Background The name evolved into over 100 different spellings in countries around the world. Nicknames ( Dan, Danny) are common in both English and Hebrew; "Dan" may also be a complete given name rather than a nickname. The name "Daniil" (Даниил) is common in Russia. Feminine versions ( Danielle, Danièle, Daniela, Daniella, Dani, Danitza) are prevalent as well. It has been particularly well-used in Ireland. The Dutch names "Daan" and "Daniël" are also variations of Daniel. A related surname ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rolling Hash
A rolling hash (also known as recursive hashing or rolling checksum) is a hash function where the input is hashed in a window that moves through the input. A few hash functions allow a rolling hash to be computed very quickly—the new hash value is rapidly calculated given only the old hash value, the old value removed from the window, and the new value added to the window—similar to the way a moving average function can be computed much more quickly than other low-pass filters. One of the main applications is the Rabin–Karp string search algorithm, which uses the rolling hash described below. Another popular application is the rsync program, which uses a checksum based on Mark Adler's adler-32 as its rolling hash. Low Bandwidth Network Filesystem (LBFS) uses a Rabin fingerprint as its rolling hash. FastCDC (Fast Content-Defined Chunking) uses a compute-efficient Gear fingerprint as its rolling hash. At best, rolling hash values are pairwise independentDaniel Lemire, Owen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tabulation Hashing
In computer science, tabulation hashing is a method for constructing universal families of hash functions by combining table lookup with exclusive or operations. It was first studied in the form of Zobrist hashing for computer games; later work by Carter and Wegman extended this method to arbitrary fixed-length keys. Generalizations of tabulation hashing have also been developed that can handle variable-length keys such as text strings. Despite its simplicity, tabulation hashing has strong theoretical properties that distinguish it from some other hash functions. In particular, it is 3-independent: every 3-tuple of keys is equally likely to be mapped to any 3-tuple of hash values. However, it is not 4-independent. More sophisticated but slower variants of tabulation hashing extend the method to higher degrees of independence. Because of its high degree of independence, tabulation hashing is usable with hashing methods that require a high-quality hash function, including hopsc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist. In other words, a ''ring'' is a set equipped with two binary operations satisfying properties analogous to those of addition and multiplication of integers. Ring elements may be numbers such as integers or complex numbers, but they may also be non-numerical objects such as polynomials, square matrices, functions, and power series. Formally, a ''ring'' is an abelian group whose operation is called ''addition'', with a second binary operation called ''multiplication'' that is associative, is distributive over the addition operation, and has a multiplicative identity element. (Some authors use the term " " with a missing i to refer to the more general structure that omits this last requirement; see .) Whether a ring is commutative (that is, whether the order in which two elements are multiplied might change the resu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
