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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 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 areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...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 \mathbb = \; * The probability distribution of the number Y=X-1 of failures before the first success, supported on \mathbb_0 = \ . 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 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 success on each trial is p, then the probability that the k-th trial is the first success is :\Pr(X = k) = (1-p)^p for k=1,2,3,4,\dots The above form of ... [...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 should 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–Eule ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rabin Fingerprint
The Rabin fingerprinting scheme (aka Polynomial fingerprinting) 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 compu ... [...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 created the C programming language and the Unix operating system and B language with long-time colleague Ken Thompson. Ritchie and Thompson were awarded the Turing Award from the Association for Computing Machinery (ACM) in 1983, the IEEE Richard W. Hamming Medal from the Institute of Electrical and Electronics Engineers (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. Early life and education 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 Harvard Un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brian Kernighan
Brian Wilson Kernighan (; born January 30, 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"). Kernighan authored many Unix programs, including ditroff. He 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel J
Daniel commonly refers to: * Daniel (given name), a masculine given name and a surname * List of people named Daniel * List of people with surname Daniel * Daniel (biblical figure) * Book of Daniel, a biblical apocalypse, "an account of the activities and visions of Daniel" Daniel may also refer to: Arts and entertainment Literature * ''Daniel'' (Old English poem), an adaptation of the Book of Daniel * ''Daniel'', a 2006 novel by Richard Adams * ''Daniel'' (Mankell novel), 2007 Music * "Daniel" (Bat for Lashes song) (2009) * "Daniel" (Elton John song) (1973) * "Daniel", a song from '' Beautiful Creature'' by Juliana Hatfield * ''Daniel'' (album), a 2024 album by Real Estate Other arts and entertainment * ''Daniel'' (1983 film), by Sidney Lumet * ''Daniel'' (2019 film), a Danish film * Daniel (comics), a character in the ''Endless'' series Businesses * Daniel (department store), in the United Kingdom * H & R Daniel, a producer of English porcelain between 1827 and 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thue–Morse Sequence
In mathematics, the Thue–Morse or Prouhet–Thue–Morse sequence is the binary sequence (an infinite sequence of 0s and 1s) that can be obtained by starting with 0 and successively appending the Boolean complement of the sequence obtained thus far. It is sometimes called the fair share sequence because of its applications to fair division or parity sequence. The first few steps of this procedure yield the strings 0, 01, 0110, 01101001, 0110100110010110, and so on, which are the prefixes of the Thue–Morse sequence. The full sequence begins: :01101001100101101001011001101001.... The sequence is named after Axel Thue, Marston Morse and (in its extended form) Eugène Prouhet. Definition There are several equivalent ways of defining the Thue–Morse sequence. Direct definition To compute the ''n''th element ''tn'', write the number ''n'' in binary. If the number of ones in this binary expansion is odd then ''tn'' = 1, if even then ''tn'' = 0. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Overflow
In computer programming, an integer overflow occurs when an arithmetic operation on integers attempts to create a numeric value that is outside of the range that can be represented with a given number of digits – either higher than the maximum or lower than the minimum representable value. The most common result of an overflow is that the least significant representable digits of the result are stored; the result is said to ''wrap'' around the maximum (i.e. modulo a power of the radix, usually two in modern computers, but sometimes ten or other number). On some processors like graphics processing units (GPUs) and digital signal processors (DSPs) which support saturation arithmetic, overflowed results would be ''clamped'', i.e. set to the minimum value in the representable range if the result is below the minimum and set to the maximum value in the representable range if the result is above the maximum, rather than wrapped around. An overflow condition may give results lead ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rolling Hash
Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding. Rolling where there is no sliding is referred to as ''pure rolling''. By definition, there is no sliding when there is a frame of reference in which all points of contact on the rolling object have the same velocity as their counterparts on the surface on which the object rolls; in particular, for a frame of reference in which the rolling plane is at rest (see animation), the instantaneous velocity of all the points of contact (for instance, a generating line segment of a cylinder) of the rolling object is zero. In practice, due to small deformations near the contact area, some sliding and energy dissipation occurs. Nevertheless, the resulting rolling resistance is much lower than sliding friction, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tabulation Hashing
A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure. Tables are widely used in communication, research, and data analysis. Tables appear in print media, handwritten notes, computer software, architectural ornamentation, traffic signs, and many other places. The precise conventions and terminology for describing tables vary depending on the context. Further, tables differ significantly in variety, structure, flexibility, notation, representation and use. Information or data conveyed in table form is said to be in tabular format (adjective). In books and technical articles, tables are typically presented apart from the main text in numbered and captioned floating blocks. Basic description A table consists of an ordered arrangement of rows and columns. This is a simplified description of the most basic kind of table. Certain considerations follow from this simplified description: * the term row has several ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
