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

A note on the complexity of the maximum edge clique partitioning problem with respect to clique number

T T Te e ec c ch h hn n ni i ic c ca a al l l R R Re e ep p po o or r rt t t A note on the complexity of the maximum edge clique partitioning problem with respect to clique number Abstract The maximum edge clique partitioning problem (Max-ECP) was considered by Dessmark et al. In this note, we give several complexity results of Max-ECP with respect to clique number, which include a new proof of the above claim

SMALL DEGENERATE SIMPLICES CAN BE BAD FOR SIMPLEX METHODS

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Workshop on Advances in Optimization

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The diameter of lattice zonotopes.

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