388 research outputs found
A primal-simplex based Tardos' algorithm
In the mid-eighties Tardos proposed a strongly polynomial algorithm for
solving linear programming problems for which the size of the coefficient
matrix is polynomially bounded by the dimension. Combining Orlin's primal-based
modification and Mizuno's use of the simplex method, we introduce a
modification of Tardos' algorithm considering only the primal problem and using
simplex method to solve the auxiliary problems. The proposed algorithm is
strongly polynomial if the coefficient matrix is totally unimodular and the
auxiliary problems are non-degenerate.Comment: 7 page
General Relativistic MHD Simulations of the Gravitational Collapse of a Rotating Star with Magnetic Field as a Model of Gamma-Ray Bursts
We have performed 2.5-dimensional general relativistic magnetohydrodynamic
(MHD) simulations of the gravitational collapse of a magnetized rotating
massive star as a model of gamma ray bursts (GRBs). This simulation showed the
formation of a disk-like structure and the generation of a jet-like outflow
inside the shock wave launched at the core bounce. We have found the jet is
accelerated by the magnetic pressure and the centrifugal force and is
collimated by the pinching force of the toroidal magnetic field amplified by
the rotation and the effect of geometry of the poloidal magnetic field. The
maximum velocity of the jet is mildly relativistic ( 0.3 c).Comment: 4 pages, 1 figure, aipTEX, contribution to the 2003 GRB Conference,
held at Santa Fe, N
A Bound for the Number of Different Basic Solutions Generated by the Simplex Method
In this short paper, we give an upper bound for the number of different basic
feasible solutions generated by the simplex method for linear programming
problems having optimal solutions. The bound is polynomial of the number of
constraints, the number of variables, and the ratio between the minimum and the
maximum values of all the positive elements of primal basic feasible solutions.
When the primal problem is nondegenerate, it becomes a bound for the number of
iterations. We show some basic results when it is applied to special linear
programming problems. The results include strongly polynomiality of the simplex
method for Markov Decision Problem by Ye and utilize its analysis.Comment: Keywords: Simplex method, Linear programming, Iteration bound, Strong
polynomiality, Basic feasible solution
A Bound for the Number of Different Basic Solutions Generated by the Simplex Method
In this short paper, we give an upper bound for the number of different basic
feasible solutions generated by the simplex method for linear programming
problems having optimal solutions. The bound is polynomial of the number of
constraints, the number of variables, and the ratio between the minimum and the
maximum values of all the positive elements of primal basic feasible solutions.
When the primal problem is nondegenerate, it becomes a bound for the number of
iterations. We show some basic results when it is applied to special linear
programming problems. The results include strongly polynomiality of the simplex
method for Markov Decision Problem by Ye and utilize its analysis.Comment: Keywords: Simplex method, Linear programming, Iteration bound, Strong
polynomiality, Basic feasible solution
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