A new kind of 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 devised. The new matroid has application in the field of inverse combinatorial optimization problems.
The Base-Matroid and Inverse Combinatorial Optimization / Dell'Amico, Mauro; F., Maffioli; F., Malucelli. - In: DISCRETE APPLIED MATHEMATICS. - ISSN 0166-218X. - STAMPA. - 128:(2003), pp. 335-353.