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Karmarkar
Narendra Krishna Karmarkar (born Circa 1956) is an Indian Mathematician. Karmarkar developed Karmarkar's algorithm. He is listed as an ISI highly cited researcher. He invented one of the first provably polynomial time algorithms for linear programming, which is generally referred to as an interior point method. The algorithm is a cornerstone in the field of Linear Programming. He published his famous result in 1984 while he was working for Bell Laboratories in New Jersey. Biography Karmarkar received his B.Tech in Electrical Engineering from IIT Bombay in 1978, Master of Science, MS from the California Institute of Technology in 1979, and PhD in Computer Science from the University of California, Berkeley in 1983 under the supervision of Richard M. Karp. Karmarkar was a post-doctoral research fellow at IBM research (1983), Member of Technical Staff and fellow at Mathematical Sciences Research Center, AT&T Bell Laboratories (1983-1998), professor of mathematics at M.I.T. (1991), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karmarkar's Algorithm
Karmarkar's algorithm is an algorithm introduced by Narendra Karmarkar in 1984 for solving linear programming problems. It was the first reasonably efficient algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice. Denoting n as the number of variables and L as the number of bits of input to the algorithm, Karmarkar's algorithm requires O(n^ L) operations on O(L) digit numbers, as compared to O(n^6 L) such operations for the ellipsoid algorithm. The runtime of Karmarkar's algorithm is thus :O(n^ L^2 \cdot \log L \cdot \log \log L) using FFT-based multiplication (see Big O notation). Karmarkar's algorithm falls within the class of interior point methods: the current guess for the solution does not follow the boundary of the feasible set as in the simplex method, but it moves through the interior of the feasible region, improving the approximation of the optimal solution by a definite fraction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the mathematical optimization, optimization of a linear objective function, subject to linear equality and linear inequality Constraint (mathematics), constraints. Its feasible region is a convex polytope, which is a set defined as the intersection (mathematics), intersection of finitely many Half-space (geometry), half spaces, each of which is defined by a linear inequality. Its objective function is a real number, real-valued affine function, affine (linear) function defined on this polyhedron. A linear programming algorithm finds a point in the polytope where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fulkerson Prize
The Fulkerson Prize for outstanding papers in the area of discrete mathematics is sponsored jointly by the Mathematical Optimization Society (MOS) and the American Mathematical Society (AMS). Up to three awards of $1,500 each are presented at each (triennial) International Symposium of the MOS. Originally, the prizes were paid out of a memorial fund administered by the AMS that was established by friends of the late Delbert Ray Fulkerson to encourage mathematical excellence in the fields of research exemplified by his work. The prizes are now funded by an endowment administered by MPS. Winners SourceMathematical Optimization Society* 1979: ** Richard M. Karp for classifying many important NP-complete problems. ** Kenneth Appel and Wolfgang Haken for the four color theorem. ** Paul Seymour for generalizing the max-flow min-cut theorem to matroids. * 1982: ** D.B. Judin, Arkadi Nemirovski, Leonid Khachiyan, Martin Grötschel, László Lovász and Alexander Schrijver for the e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interior Point Method
Interior-point methods (also referred to as barrier methods or IPMs) are a certain class of algorithms that solve linear and nonlinear convex optimization problems. An interior point method was discovered by Soviet mathematician I. I. Dikin in 1967 and reinvented in the U.S. in the mid-1980s. In 1984, Narendra Karmarkar developed a method for linear programming called Karmarkar's algorithm, which runs in provably polynomial time and is also very efficient in practice. It enabled solutions of linear programming problems that were beyond the capabilities of the simplex method. Contrary to the simplex method, it reaches a best solution by traversing the interior of the feasible region. The method can be generalized to convex programming based on a self-concordant barrier function used to encode the convex set. Any convex optimization problem can be transformed into minimizing (or maximizing) a linear function over a convex set by converting to the epigraph form. The idea of encodi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by multinational company Nokia. With headquarters located in Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world. Researchers working at Bell Laboratories are credited with the development of radio astronomy, the transistor, the laser, the photovoltaic cell, the charge-coupled device (CCD), information theory, the Unix operating system, and the programming languages B, C, C++, S, SNOBOL, AWK, AMPL, and others. Nine Nobel Prizes have been awarded for work completed at Bell Laboratories. Bell Labs had its origin in the complex corporate organization of the Bell System telephone conglomerate. In the late 19th century, the laboratory began as the Western Electric Engineering Department, l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bell Laboratories
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984), then AT&T Bell Laboratories (1984–1996) and Bell Labs Innovations (1996–2007), is an American industrial research and scientific development company owned by multinational company Nokia. With headquarters located in Murray Hill, New Jersey, the company operates several laboratories in the United States and around the world. Researchers working at Bell Laboratories are credited with the development of radio astronomy, the transistor, the laser, the photovoltaic cell, the charge-coupled device (CCD), information theory, the Unix operating system, and the programming languages B, C, C++, S, SNOBOL, AWK, AMPL, and others. Nine Nobel Prizes have been awarded for work completed at Bell Laboratories. Bell Labs had its origin in the complex corporate organization of the Bell System telephone conglomerate. In the late 19th century, the laboratory began as the Western Electric Engineering Department, l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
California Institute Of Technology
The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasionally referred to as "CIT", most notably in its alma mater, but this is uncommon. is a private research university in Pasadena, California. Caltech is ranked among the best and most selective academic institutions in the world, and with an enrollment of approximately 2400 students (acceptance rate of only 5.7%), it is one of the world's most selective universities. The university is known for its strength in science and engineering, and is among a small group of institutes of technology in the United States which is primarily devoted to the instruction of pure and applied sciences. The institution was founded as a preparatory and vocational school by Amos G. Throop in 1891 and began attracting influential scientists such as George Ellery H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of California, Berkeley
The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant university and the founding campus of the University of California system. Its fourteen colleges and schools offer over 350 degree programs and enroll some 31,800 undergraduate and 13,200 graduate students. Berkeley ranks among the world's top universities. A founding member of the Association of American Universities, Berkeley hosts many leading research institutes dedicated to science, engineering, and mathematics. The university founded and maintains close relationships with three national laboratories at Berkeley, Livermore and Los Alamos, and has played a prominent role in many scientific advances, from the Manhattan Project and the discovery of 16 chemical elements to breakthroughs in computer science and genomics. Berkeley is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paris Kanellakis Award
The Paris Kanellakis Theory and Practice Award is granted yearly by the Association for Computing Machinery (ACM) to honor "specific theoretical accomplishments that have had a significant and demonstrable effect on the practice of computing". It was instituted in 1996, in memory of Paris C. Kanellakis, a computer scientist who died with his immediate family in an airplane crash in South America in 1995 (American Airlines Flight 965). The award is accompanied by a prize of $10,000 and is endowed by contributions from Kanellakis's parents, with additional financial support provided by four ACM Special Interest Groups (SIGACT, SIGDA, SIGMOD, and SIGPLAN), the ACM SIG Projects Fund, and individual contributions. Winners See also * List of computer science awards This list of computer science awards is an index to articles on notable awards related to computer science. It includes lists of awards by the Association for Computing Machinery, the Institute of Electrical and Electronic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Time
In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expresse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs. The society is one of the four parts of the Joint Policy Board for Mathematics and a member of the Conference Board of the Mathematical Sciences. History The AMS was founded in 1888 as the New York Mathematical Society, the brainchild of Thomas Fiske, who was impressed by the London Mathematical Society on a visit to England. John Howard Van Amringe was the first president and Fiske became secretary. The society soon decided to publish a journal, but ran into some resistance, due to concerns about competing with the American Journal of Mathematics. The result was the ''Bulletin of the American Mathematical Society'', with Fiske as editor-in-chief. The de facto journal, as intended, was influential in in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Programming Society
The Mathematical Optimization Society (MOS), known as the Mathematical Programming Society until 2010, . is an international association of researchers active in . The MOS encourages the research, development, and use of optimization—including , [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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