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Flajolet–Martin Algorithm
The Flajolet–Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem). The algorithm was introduced by Philippe Flajolet and G. Nigel Martin in their 1984 article "Probabilistic Counting Algorithms for Data Base Applications". Later it has been refined in "LogLog counting of large cardinalities" by Marianne Durand and Philippe Flajolet, and " HyperLogLog: The analysis of a near-optimal cardinality estimation algorithm" by Philippe Flajolet et al. In their 2010 article "An optimal algorithm for the distinct elements problem", Daniel M. Kane, Jelani Nelson and David P. Woodruff give an improved algorithm, which uses nearly optimal space and has optimal ''O''(1) update and reporting times. The algorithm Assume that we are given a hash function \mathrm(x) that maps input x to integers in the ra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Count-distinct Problem
In computer science, the count-distinct problem (also known in applied mathematics as the cardinality estimation problem) is the problem of finding the number of distinct elements in a data stream with repeated elements. This is a well-known problem with numerous applications. The elements might represent IP addresses of packets passing through a router, unique visitors to a web site, elements in a large database, motifs in a DNA sequence, or elements of RFID/sensor networks. Formal definition : Instance: Consider a stream of elements x_1, x_2, \ldots, x_s with repetitions. Let n denote the number of distinct elements in the stream, with the set of distinct elements represented as \. : Objective: Find an estimate \widehat of n using only m storage units, where m \ll n . An example of an instance for the cardinality estimation problem is the stream: a,b,a,c,d,b,d . For this instance, n = , \left\, = 4 . Naive solution The naive solution to the problem is as follows: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Philippe Flajolet
Philippe Flajolet (; 1 December 1948 – 22 March 2011) was a French computer scientist. Biography A former student of École Polytechnique, Philippe Flajolet received his PhD in computer science from University Paris Diderot in 1973 and state doctorate from Paris-Sud 11 University in 1979. Most of Philippe Flajolet's research work was dedicated towards general methods for analyzing the computational complexity of algorithms, including the theory of average-case complexity. He introduced the theory of analytic combinatorics. With Robert Sedgewick of Princeton University, he wrote the first book-length treatment of the topic, the 2009 book entitled ''Analytic Combinatorics''. In 1993, together with Rainer Kemp, Helmut Prodinger and Robert Sedgewick, Flajolet initiated the successful series of workshops and conferences which was key to the development of a research community around the analysis of algorithms, and which evolved into the AofA—International Meeting on Combinatoria ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Marianne Durand
Marianne () has been the national personification of the French Republic since the French Revolution, as a personification of liberty, equality, fraternity and reason, as well as a portrayal of the Goddess of Liberty. Marianne is displayed in many places in France and holds a place of honour in town halls and law courts. She is depicted in the ''Triumph of the Republic'', a bronze sculpture overlooking the Place de la Nation in Paris, as well as represented with another Parisian statue on the Place de la République. Her profile stands out on the official government logo of the country, and appears on French euro coins and on French postage stamps. She was also featured on the former franc currency and is officially used on most government documents. Marianne is a significant republican symbol; her French monarchist equivalent is often Joan of Arc. As a national icon Marianne represents opposition to monarchy and the championship of freedom and democracy against all forms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
HyperLogLog
HyperLogLog is an algorithm for the count-distinct problem, approximating the number of distinct elements in a multiset. Calculating the ''exact'' cardinality of the distinct elements of a multiset requires an amount of memory proportional to the cardinality, which is impractical for very large data sets. Probabilistic cardinality estimators, such as the HyperLogLog algorithm, use significantly less memory than this, but can only approximate the cardinality. The HyperLogLog algorithm is able to estimate cardinalities of > 109 with a typical accuracy (standard error) of 2%, using 1.5 kB of memory. HyperLogLog is an extension of the earlier LogLog algorithm, itself deriving from the 1984 Flajolet–Martin algorithm. Terminology In the original paper by Flajolet ''et al.'' and in related literature on the count-distinct problem, the term "cardinality" is used to mean the number of distinct elements in a data stream with repeated elements. However in the theory of multi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Nancy, France
Nancy is the Prefectures in France, prefecture of the northeastern Departments of France, French department of Meurthe-et-Moselle. It was the capital of the Duchy of Lorraine, which was Lorraine and Barrois, annexed by France under King Louis XV in 1766 and replaced by a Provinces of France, province, with Nancy maintained as capital. Following its rise to prominence in the Age of Enlightenment, it was nicknamed the "capital of Eastern France" in the late 19th century. The metropolitan area of Nancy had a population of 508,793 inhabitants as of 2021, making it the 16th-largest functional area (France), functional urban area in France and Lorraine's largest. The population of the city of Nancy proper is 104,387 (2022). The motto of the city is —a reference to the thistle, which is a symbol of Lorraine. Place Stanislas, a large square built between 1752 and 1756 by architect Emmanuel Héré under the direction of Stanislaus I of Poland to link the medieval old town of Nancy and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Daniel M
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 18 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Jelani Nelson
Jelani Osei Nelson (; born June 28, 1984) is an American Professor of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He won the 2014 Presidential Early Career Award for Scientists and Engineers. Nelson is the creator of ''AddisCoder'', a computer science summer program for Ethiopian high school students in Addis Ababa. Early life and education Nelson was born to an Ethiopian mother and an African-American father in Los Angeles, then grew up in St. Thomas, U.S. Virgin Islands. He studied mathematics and computer science at the Massachusetts Institute of Technology and remained there to complete his doctoral studies in computer science. His Master's dissertation, ''External-Memory Search Trees with Fast Insertions'', was supervised by Bradley C. Kuszmaul and Charles E. Leiserson. He was a member of the theory of computation group, working on efficient algorithms for massive datasets. His doctoral dissertation, ''Sketching and Streaming Hig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
David P
David (; , "beloved one") was a king of ancient Israel and Judah and the third king of the United Monarchy, according to the Hebrew Bible and Old Testament. The Tel Dan stele, an Aramaic-inscribed stone erected by a king of Aram-Damascus in the late 9th/early 8th centuries BCE to commemorate a victory over two enemy kings, contains the phrase (), which is translated as " House of David" by most scholars. The Mesha Stele, erected by King Mesha of Moab in the 9th century BCE, may also refer to the "House of David", although this is disputed. According to Jewish works such as the '' Seder Olam Rabbah'', '' Seder Olam Zutta'', and ''Sefer ha-Qabbalah'' (all written over a thousand years later), David ascended the throne as the king of Judah in 885 BCE. Apart from this, all that is known of David comes from biblical literature, the historicity of which has been extensively challenged,Writing and Rewriting the Story of Solomon in Ancient Israel; by Isaac Kalimi; page 32; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Hash Function
A hash function is any Function (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called ''hash values'', ''hash codes'', (''hash/message'') ''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 s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Discrete Uniform Distribution
In probability theory and statistics, the discrete uniform distribution is a symmetric probability distribution wherein each of some finite whole number ''n'' of outcome values are equally likely to be observed. Thus every one of the ''n'' outcome values has equal probability 1/''n''. Intuitively, a discrete uniform distribution is "a known, finite number of outcomes all equally likely to happen." A simple example of the discrete uniform distribution comes from throwing a fair six-sided die. The possible values are 1, 2, 3, 4, 5, 6, and each time the die is thrown the probability of each given value is 1/6. If two dice were thrown and their values added, the possible sums would not have equal probability and so the distribution of sums of two dice rolls is not uniform. Although it is common to consider discrete uniform distributions over a contiguous range of integers, such as in this six-sided die example, one can define discrete uniform distributions over any finite set. Fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Multiset
In mathematics, a multiset (or bag, or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements. The number of instances given for each element is called the ''multiplicity'' of that element in the multiset. As a consequence, an infinite number of multisets exist that contain only elements and , but vary in the multiplicities of their elements: * The set contains only elements and , each having multiplicity 1 when is seen as a multiset. * In the multiset , the element has multiplicity 2, and has multiplicity 1. * In the multiset , and both have multiplicity 3. These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to ''tuples'', the order in which elements are listed does not matter in discriminating multisets, so and denote the same multiset. To distinguish between sets and multisets, a notat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
