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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
- ISSAC
- 1996

The problem of computing the greatest common divisor (gcd) of two polynomials ~, g ~ A[z], A being a unique factorization domain, is well understood and there area number of efficient algorithms for computing polynomial gcds beginning with the the work of Collins and Brown [3, 4, 9]. In this paper, we investigate the problem of finding approximate gcds.… (More)

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

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

We apply the zero-one integer programming algorithm described in Karmarkar [12] and Karmarkar, Resende and Ramakrishnan [13] to solve randomly generated instances of the satisfiability problem (SAT). The interior point algorithm is briefly reviewed and shown to be easily adapted to solve large instances of SAT. Hundreds of instances of SAT (having from 100… (More)

- Narendra Karmarkar, K. G. Ramakrishnan
- Math. Program.
- 1991

This paper gives computational results for an efficient implementation of a variant of dual projective algorithm for linear programming. The implementation uses the preconditioned conjugate gradient method for computing projections. Our computational experience reported in this paper indicates that this algorithm has potential as an alternative for solving… (More)

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

- 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 polytope 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)