Complexity of linear programming

Complexity of Linear Programming

The complexity of linear programming is discussed in the "integer" and "real number" models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation. Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has u...

Linear Programming , Complexity

Computational complexity of parametric linear programming

where A is a matrix of order m × p and rank m, and A is a real valued parameter. It may be required to solve this problem for all real values of A, or for all values of A in some specified interval of the real line. f(A) is a piecewise linear convex function in A. The simplex algorithm for this parametric linear program partitions the real line into intervals, each interval being the optimality...

On the complexity of linear programming

This is a partial survey of results on the complexity of the linear programming problem since the ellipsoid method. The main topics are polynomial and strongly polynomial algorithms, probabilistic analysis of simplex algorithms, and recent interior point methods.

The Parallel Complexity of Positive Linear Programming

In this paper we study the parallel complexity of Positive Linear Programming (PLP), i.e. the special case of Linear Programming in packing/covering form where the input constraint matrix and constraint vector consist entirely of positive entries. We show that the problem of exactly solving PLP is P-complete. Luby and Nisan gave an NC approximation algorithm for PLP, and their algorithm can be ...