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Bitonic Tour
In computational geometry, a bitonic tour of a set of point sites in the Euclidean plane is a closed polygonal chain that has each site as one of its vertices, such that any vertical line crosses the chain at most twice. Optimal bitonic tours The optimal bitonic tour is a bitonic tour of minimum total length. It is a standard exercise in dynamic programming to devise a polynomial time algorithm that constructs the optimal bitonic tour. Although the usual method for solving it in this way takes time O(n^2), a faster algorithm with time O(n\log^2 n) is known. The problem of constructing optimal bitonic tours is often credited to Jon L. Bentley, who published in 1990 an experimental comparison of many heuristics for the traveling salesman problem; however, Bentley's experiments do not include bitonic tours. The first publication that describes the bitonic tour problem appears to be a different 1990 publication, the first edition of the textbook ''Introduction to Algorithms'' by Thom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bitonic Tour
In computational geometry, a bitonic tour of a set of point sites in the Euclidean plane is a closed polygonal chain that has each site as one of its vertices, such that any vertical line crosses the chain at most twice. Optimal bitonic tours The optimal bitonic tour is a bitonic tour of minimum total length. It is a standard exercise in dynamic programming to devise a polynomial time algorithm that constructs the optimal bitonic tour. Although the usual method for solving it in this way takes time O(n^2), a faster algorithm with time O(n\log^2 n) is known. The problem of constructing optimal bitonic tours is often credited to Jon L. Bentley, who published in 1990 an experimental comparison of many heuristics for the traveling salesman problem; however, Bentley's experiments do not include bitonic tours. The first publication that describes the bitonic tour problem appears to be a different 1990 publication, the first edition of the textbook ''Introduction to Algorithms'' by Thom ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ron Rivest
Ronald Linn Rivest (; born May 6, 1947) is a cryptographer and an Institute Professor at MIT. He is a member of MIT's Department of Electrical Engineering and Computer Science (EECS) and a member of MIT's Computer Science and Artificial Intelligence Laboratory (CSAIL). His work has spanned the fields of algorithms and combinatorics, cryptography, machine learning, and election integrity. Rivest is one of the inventors of the RSA algorithm (along with Adi Shamir and Len Adleman). He is the inventor of the symmetric key encryption algorithms RC2, RC4, RC5, and co-inventor of RC6. The "RC" stands for "Rivest Cipher", or alternatively, "Ron's Code". (RC3 was broken at RSA Security during development; similarly, RC1 was never published.) He also authored the MD2, MD4, MD5 and MD6 cryptographic hash functions. Education Rivest earned a Bachelor's degree in Mathematics from Yale University in 1969, and a Ph.D. degree in Computer Science from Stanford University in 1974 for rese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mendoza, Argentina
Mendoza (, ), officially the City of Mendoza ( es, Ciudad de Mendoza) is the capital of the province of Mendoza in Argentina. It is located in the northern-central part of the province, in a region of foothills and high plains, on the eastern side of the Andes. As of the , Mendoza had a population of 115,041 with a metropolitan population of 1,055,679, making Greater Mendoza the fourth largest census metropolitan area in the country. Ruta Nacional 7, the major road running between Buenos Aires and Santiago, runs through Mendoza. The city is a frequent stopover for climbers on their way to Aconcagua (the highest mountain in the Western and Southern Hemispheres) and for adventure travelers interested in mountaineering, hiking, horse riding, rafting, and other sports. In the winter, skiers come to the city for easy access to the Andes. Two of the main industries of the Mendoza area are olive oil production and Argentine wine. The region around Greater Mendoza is the largest win ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
International Olympiad In Informatics
The International Olympiad in Informatics (IOI) is an annual competitive programming and one of the International Science Olympiads for secondary school students. It is the second largest science olympiad, after International Mathematical Olympiad, in terms of number of participating countries (88 at IOI 2022). The first IOI was held in 1989 in Pravetz, Bulgaria. The contest consists of two days of computer programming/coding and problem-solving of algorithmic nature. To deal with problems involving very large amounts of data, it is necessary to have not only programmers, "but also creative coders, who can dream up what it is that the programmers need to tell the computer to do. The hard part isn't the programming, but the mathematics underneath it." Students at the IOI compete on an individual basis, with up to four students competing from each participating country (with 81 countries in 2012). Students in the national teams are selected through national computing contests, such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lexicographical Order
In mathematics, the lexicographic or lexicographical order (also known as lexical order, or dictionary order) is a generalization of the alphabetical order of the dictionaries to sequences of ordered symbols or, more generally, of elements of a totally ordered set. There are several variants and generalizations of the lexicographical ordering. One variant applies to sequences of different lengths by comparing the lengths of the sequences before considering their elements. Another variant, widely used in combinatorics, orders subsets of a given finite set by assigning a total order to the finite set, and converting subsets into increasing sequences, to which the lexicographical order is applied. A generalization defines an order on a Cartesian product of partially ordered sets; this order is a total order if and only if all factors of the Cartesian product are totally ordered. Motivation and definition The words in a lexicon (the set of words used in some language) have a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygonalization
In computational geometry, a polygonalization of a finite set of points in the Euclidean plane is a simple polygon with the given points as its vertices. A polygonalization may also be called a polygonization, simple polygonalization, Hamiltonian polygon, non-crossing Hamiltonian cycle, or crossing-free straight-edge spanning cycle. Every point set that does not lie on a single line has at least one polygonalization, which can be found in polynomial time. For points in convex position, there is only one, but for some other point sets there can be exponentially many. Finding an optimal polygonalization under several natural optimization criteria is a hard problem, including as a special case the travelling salesman problem. The complexity of counting all polygonalizations remains unknown. Definition A polygonalization is a simple polygon having a given set of points in the Euclidean plane as its set of vertices. A polygon may be described by a cyclic order on its vertices, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Traveling Salesman Problem
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?" It is an NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem and the vehicle routing problem are both generalizations of TSP. In the theory of computational complexity, the decision version of the TSP (where given a length ''L'', the task is to decide whether the graph has a tour of at most ''L'') belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (but no more than exponentially) with the number of cities. The problem was first formulated in 1930 and is one of the most intensively studied p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MIT Press
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962. History The MIT Press traces its origins back to 1926 when MIT published under its own name a lecture series entitled ''Problems of Atomic Dynamics'' given by the visiting German physicist and later Nobel Prize winner, Max Born. Six years later, MIT's publishing operations were first formally instituted by the creation of an imprint called Technology Press in 1932. This imprint was founded by James R. Killian, Jr., at the time editor of MIT's alumni magazine and later to become MIT president. Technology Press published eight titles independently, then in 1937 entered into an arrangement with John Wiley & Sons in which Wiley took over marketing and editorial responsibilities. In 1962 the association with Wiley came to an end after a further 125 titles had been published. The press acquired its modern name af ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clifford Stein
Clifford Seth Stein (born December 14, 1965), a computer scientist, is a professor of industrial engineering and operations research at Columbia University in New York, NY, where he also holds an appointment in the Department of Computer Science. Stein is chair of the Industrial Engineering and Operations Research Department at Columbia University. Prior to joining Columbia, Stein was a professor at Dartmouth College in New Hampshire. Stein's research interests include the design and analysis of algorithms, combinatorial optimization, operations research, network algorithms, scheduling, algorithm engineering and computational biology. Stein has published many influential papers in the leading conferences and journals in his fields of research, and has occupied a variety of editorial positions including in the journals ''ACM Transactions on Algorithms'', ''Mathematical Programming'', ''Journal of Algorithms'', ''SIAM Journal on Discrete Mathematics'' and ''Operations Resear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles E
Charles is a masculine given name predominantly found in English and French speaking countries. It is from the French form ''Charles'' of the Proto-Germanic name (in runic alphabet) or ''*karilaz'' (in Latin alphabet), whose meaning was "free man". The Old English descendant of this word was '' Ċearl'' or ''Ċeorl'', as the name of King Cearl of Mercia, that disappeared after the Norman conquest of England. The name was notably borne by Charlemagne (Charles the Great), and was at the time Latinized as ''Karolus'' (as in ''Vita Karoli Magni''), later also as '' Carolus''. Some Germanic languages, for example Dutch and German, have retained the word in two separate senses. In the particular case of Dutch, ''Karel'' refers to the given name, whereas the noun ''kerel'' means "a bloke, fellow, man". Etymology The name's etymology is a Common Germanic noun ''*karilaz'' meaning "free man", which survives in English as churl (< Old English ''ċeorl''), which developed its depr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Geometry
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity. Analysis of algorithms, Computational complexity is central to computational geometry, with great practical significance if algorithms are used on very large datasets containing tens or hundreds of millions of points. For such sets, the difference between O(''n''2) and O(''n'' log ''n'') may be the difference between days and seconds of computation. The main impetus for the development of computational geometry as a discipline was progress in computer graphics and computer-aided design and manufacturing (Computer-aided design, CAD/Compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thomas H
Thomas may refer to: People * List of people with given name Thomas * Thomas (name) * Thomas (surname) * Saint Thomas (other) * Thomas Aquinas (1225–1274) Italian Dominican friar, philosopher, and Doctor of the Church * Thomas the Apostle * Thomas (bishop of the East Angles) (fl. 640s–650s), medieval Bishop of the East Angles * Thomas (Archdeacon of Barnstaple) (fl. 1203), Archdeacon of Barnstaple * Thomas, Count of Perche (1195–1217), Count of Perche * Thomas (bishop of Finland) (1248), first known Bishop of Finland * Thomas, Earl of Mar (1330–1377), 14th-century Earl, Aberdeen, Scotland Geography Places in the United States * Thomas, Illinois * Thomas, Indiana * Thomas, Oklahoma * Thomas, Oregon * Thomas, South Dakota * Thomas, Virginia * Thomas, Washington * Thomas, West Virginia * Thomas County (other) * Thomas Township (other) Elsewhere * Thomas Glacier (Greenland) Arts, entertainment, and media * ''Thomas'' (Burton novel) 1969 novel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
