  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.
