The base-matroid and inverse combinatorial optimization problems Original Research Article

A new matroid is introduced: this matroid is defined starting from any matroid and one of its bases, hence we call it base-matroid. Besides some properties of the base-matroid, a non-trivial algorithm for the solution of the related matroid optimization problem is presented. The new matroid has application in the field of inverse combinatorial optimization problems. We discuss in detail the LP formulation of the inverse matroid optimization problem and we propose an efficient algorithm for computing its primal and dual solutions.