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We show that the simplex method with Dantzig’s pivoting rule may require an exponential number of iterations over two highly degenerate instances. The feasible region of the first instance is a full dimensional simplex, and a single point for the second one. In addition, the entries of the constraint matrix, the right-hand-side vector, and the cost vector are {0, 1, 2}-valued. Those instances, with few vertices and small input data length, illustrate the impact of degeneracy on simplex methods.

SMALL DEGENERATE SIMPLICES CAN BE BAD FOR SIMPLEX METHODS