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- Narendra Karmarkar
- STOC
- 1984

We present a new polynomial-time algorithm for linear programming. The running-time of this algorithm is <italic>O</italic>(<italic>n</italic><supscrpt>3-5</supscrpt><italic>L</italic><supscrpt>2</supscrpt>), as compared to <italic>O</italic>(<italic>n</italic><supscrpt>6</supscrpt><italic>L</italic><supscrpt>2</supscrpt>) for the ellipsoid algorithm. We… (More)

- Narendra Karmarkar, Richard M. Karp
- 23rd Annual Symposium on Foundations of Computer…
- 1982

We present several polynomial-time approximation algorithms for the one-dimensional bin-packing problem. using a subroutine to solve a certain linear programming relaxation of the problem. Our main results are as follows: There is a polynomial-time algorithm A such that A(I) ≤ OPT(I) + O(log2 OPT(I)). There is a polynomial-time algorithm A such… (More)

- Narendra Karmarkar, Yagati N. Lakshman
- J. Symb. Comput.
- 1998

- Anil P. Kamath, Narendra Karmarkar, K. G. Ramakrishnan, Mauricio G. C. Resende
- Math. Program.
- 1992

- Narendra Karmarkar, Yagati N. Lakshman
- ISSAC
- 1996

- Ilan Adler, Narendra Karmarkar, Mauricio G. C. Resende, Geraldo Veiga
- INFORMS Journal on Computing
- 1989

- Narendra Karmarkar, Richard M. Karp, Richard J. Lipton, László Lovász, Michael Luby
- SIAM J. Comput.
- 1993

Let A be an nn matrix with 0-1 valued entries, and let per(A) be the permanent of A. We describe a Monte-Carlo algorithm which produces a \good in the relative sense" estimate of per(A) and has running time poly(n)2 n=2 , where poly(n) denotes a function that grows polynomially with n.

- Narendra Karmarkar, Mauricio G. C. Resende, K. G. Ramakrishnan
- Math. Program.
- 1991

We present an interior point approach to the zero-one integer programming feasibility problem based on the minimization of a nonconvex potential function. Given a poly-tope defined by a set of linear inequalities, this procedure generates a sequence of strict interior points of this polytope, such that each consecutive point reduces the value of the… (More)

- Ilan Adler, Mauricio G. C. Resende, Geraldo Veiga, Narendra Karmarkar
- Math. Program.
- 1989

This paper describes the implementation of power series dual affine scaling variants of Karmarkar's algorithm for linear programming. Based on a continuous version of Karmarkar's algorithm, two variants resulting from first and second order approximations of the continuous trajectory are implemented and tested. Linear programs are expressed in an inequality… (More)

- Narendra Karmarkar
- SC
- 1991

Many problems in scientific cotnputation involve sparse matrices. While dense matrix computations can be parallelized relatively easily, sparse matrices with arbitrary or irregular structure pose a real challenge to the design of highly parallel machines. In this paper we propose a new parallel architecture for sparse matrix computation based on finite… (More)