A primal-simplex based Tardos’ algorithm

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 in the dimension of the input. Combining Orlin’s primal-basedmodification andMizuno’s use of the simplex method, we introduce a modification of Tardos’ algorithm considering only the primal problem and using the simplex ...

An enhanced primal-simplex based Tardos’ algorithm

The authors recently proposed a simplex-based Tardos’ algorithm which is strongly polynomial if the coefficient matrix is totally unimodular and the auxiliary problems are non-degenerate. Motivated by the algorithmic practically of such methods, we introduce a modification which circumvents the determination of the largest sub-determinant while keeping the same theoretical performance. Assuming...

A parallel primal-dual simplex algorithm

Recently, the primal–dual simplex method has been used to solve linear programs with a large number of columns. We present a parallel primal–dual simplex algorithm that is capable of solving linear programs with at least an order of magnitude more columns than the previous work. The algorithm repeatedly solves several linear programs in parallel and combines the dual solutions to obtain a new d...

A Faster Primal Network Simplex Algorithm

We present a faster implementation of the polynomial time primal simplex algorithm due to Orlin [23]. His algorithm requires O(nm min{log(nC), m log n}) pivots and O(n m · min{log nC, m log n}) time. The bottleneck operations in his algorithm are performing the relabeling operations on nodes, selecting entering arcs for pivots, and performing the pivots. We show how to speed up these operations...

An Intro to LP and the Simplex Algorithm Primal Simplex