Monotone Diameter of Bisubmodular Polyhedra

Finding sharp bounds on the diameter of polyhedra is a fundamental problem in discrete mathematics and computational geometry. In particular, the monotone diameter and height play an important role in determining the number of iterations by operating the pivot rule of the simplex method for linear programming. In this study, for a d -dimensional polytope defined by at most 3 d - 1 linear inequality induced by functions called bisubmodular, we prove that the diameter, monotone diameter, and height are coincide, and the tight upper bound is d 2 .