About: Karmarkar's algorithm

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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 as the number of variables and as the number of bits of input to the algorithm, Karmarkar's algorithm requires operations on digit numbers, as compared to such operations for the ellipsoid algorithm. The runtime of Karmarkar's algorithm is thus

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rdfs:label	Karmarkar's algorithm (en)
rdfs:comment	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 as the number of variables and as the number of bits of input to the algorithm, Karmarkar's algorithm requires operations on digit numbers, as compared to such operations for the ellipsoid algorithm. The runtime of Karmarkar's algorithm is thus (en)
sameAs	Karmarkar's algorithm Karmarkar's algorithm
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Subject	Articles with example pseudocode Software patent law Linear programming Optimization algorithms and methods
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Karmarkar's_algorithm?oldid=1068118862&ns=0
Wikipage page ID	3736667 (xsd:integer)
page length (characters) of wiki page	17189 (xsd:nonNegativeInteger)
Wikipage revision ID	1068118862 (xsd:integer)
Link from a Wikipage to another Wikipage	Numerical analysis Prior art Projective geometry Ron Rivest Supreme Court of the United States United States Department of Defense AT&T Affine scaling Affine transformation Algorithm Barrier function Bell Labs Big O notation Articles with example pseudocode Software patent law Linear programming Optimization algorithms and methods Diamond v. Diehr Narendra Karmarkar Linear programming Public domain Time complexity Combinatorica Software patent Soviet Union Ellipsoid method Gottschalk v. Benson IBM IBM Research Schönhage–Strassen algorithm Symposium on Theory of Computing Feasible region Interior-point method Vector processor Stanford University Mayo Collaborative Services v. Prometheus Laboratories, Inc. Multiprocessing RSA (cryptosystem) Simplex algorithm dbr:Philip_Gill dbr:Projected_Newton_barrier_method
has abstract	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 as the number of variables and as the number of bits of input to the algorithm, Karmarkar's algorithm requires operations on digit numbers, as compared to such operations for the ellipsoid algorithm. The runtime of Karmarkar's algorithm is thus 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 with every iteration, and converging to an optimal solution with rational data. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Karmarkar's_algorithm
is Wikipage redirect of	Karmarkar's interior-point algorithm Karmarkar algorithm Karmarkar interior-point algorithm Projective method
is Link from a Wikipage to another Wikipage of	List of terms relating to algorithms and data structures Affine scaling Bell Labs Bhave High School California Institute of Technology Narendra Karmarkar Criss-cross algorithm Linear programming List of Indian Americans List of numerical analysis topics List of people from Pune List of software patents Combinatorica List of Marathi people in science, engineering and technology List of algorithms List of computer scientists Ellipsoid method Fulkerson Prize Interior-point method John von Neumann Klee–Minty cube Karmarkar's interior-point algorithm Karmarkar algorithm Karmarkar interior-point algorithm
is known for of	Narendra Karmarkar
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Karmarkar's_algorithm

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