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)
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)
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.
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)
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)
We apply the zero-one integer programming algorithm described in Karmarkar  and Karmarkar, Resende and Ramakrishnan  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)