N. Karmarkar, "A new polynomial-( algorithm for linear programming", Combinatorica 4 (1984) 373--395.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a bounded number (E and E 0 ) of objects in our world, the size of the system becomes linear w.r.t. the number of integrity constraints jICj. Under these particular circumstances the system can be solved in polynomial time w.r.t. jICj by classical linear programming algorithms [Khachian 1979; Karmarkar 1984]. 8. RELATED WORK 8.1 Work on Uncertainty There has been an incredible amount of work on uncertainty in knowledge based and database systems [Shafer and Pearl 1990] However, almost all this work assumes that we are reasoning with logic or with Bayesian nets [Koller 1998] and most work ....

Karmarkar, N. 1984. A New Polynomial Algorithm for Linear Programming. Combinatorica 4, 373-395.

....interior of the constraint region throughout the solution procedure, the original mathematical programming problem essentially becomes an unconstrained system of equations. This idea is of course a central element in many interior point methods, including the one originally proposed by Karmarkar [18]. One of the central ideas in the recent development of interior point methods is the path of centers of the feasible region. This path was first studied by McLinden [31] and later by several authors [2, 3, 32, 47] The idea of approximately tracing the central path has led to the development of ....

N. Karmarkar, "A new polynomial algorithm for linear programming", Combinatorica 4 (1984) 373-395.

....inequational and equational constraints, or systems of them, has been widely investigated starting from the ancient Greeks. Such constraints arise in various areas of computer science and eOEcient algorithms are well known for solving systems of linear constraints over reals, rational numbers [20, 19] and integers [6, 27] Unfortunately, restricting the domain to the natural numbers makes the problem much more diOEcult and the algorithms in the previous class are no longer suitable. In the recent past, several works, related to the automatic deduction framework, have shown the key role of ....

N. Karmarkar. A new polynomial algorithm for linear programming. In Proceedings of the 16th Annual ACM Symposium on Theory of Computing, pages 302311, New York, 1984. Revised version: Combinatorica 4 (1984),373-395.

....of inputs, a certain variant of the method runs in polynomial time. Subsequently, under a different model, a bound of O(m 2 ) was proven by Todd [46] Adler and Megiddo [2] and Adler, Karp and Shamir [1] A new polynomial time algorithm for linear programming was proposed by Karmarkar [24] in 1984. His algorithm works on the problem in the form: Minimize c T x subject to Ax = 0 e T x = 1 x 0 where e = 1; 1) T 2 R n , assuming (without loss of generality) that the minimum equals 0 and Ae = 0. Karmarkar s algorithm generates a sequence of points in the interior ....

N. Karmarkar, "A new polynomial algorithm for linear programming," Combinatorica 4 (1984) 373--395.

....inequational and equational constraints, or systems of them, has been widely investigated starting from the ancient Greeks. Such constraints arise in various areas of computer science and efficient algorithms are well known for solving systems of linear constraints over reals, rational numbers [19,18] and integers [6,26] Unfortunately, restricting the domain to the natural numbers makes the problem much more difficult and the algorithms in the previous class are no longer suitable. 1 This work was partly supported by the European Contract SOL HCM No CHRX CT92 0053 Preprint submitted to ....

N. Karmarkar. A new polynomial algorithm for linear programming. In Proceedings of the 16th Annual ACM Symposium on Theory of Computing, pages 302--311, New York, 1984. Revised version: Combinatorica 4 (1984),373395.

....inequational and equational constraints, or systems of them, has been widely investigated starting from the ancient Greeks. Such constraints arise in various areas of computer science and efficient algorithms are well known for solving systems of linear constraints over reals, rational numbers [18, 17] and integers [5, 25] Unfortunately, restricting the domain to the natural numbers makes the problem much more difficult and the algorithms in the previous class are no longer suitable. In the recent past, several works, related to the automatic deduction framework, have shown the key role of ....

N. Karmarkar. A new polynomial algorithm for linear programming. In Proceedings of the 16th Annual ACM Symposium on Theory of Computing, pages 302--311, New York, 1984. Revised version: Combinatorica 4 (1984),373-395.

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N. Karmarkar, "A new polynomial-( algorithm for linear programming", Combinatorica 4 (1984) 373--395.

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