The base-matroid and inverse combinatorial optimization problems

Authors:
Mauro Dell'Amico;Francesco Maffioli;Federico Malucelli
Affiliations:
Dipartimento di Scienze e Metodi dell'Ingegneria, Università di Modena e Reggio Emilia, Viale Allegri, 13, 42100 Reggio Emilia, Italy;Dipartimento di Elettronica e Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy;Dipartimento di Elettronica e Informazione, Politecnico di Milano, Via Ponzio 34/5, 20133 Milano, Italy
Venue:
Discrete Applied Mathematics
Year:
2003

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Abstract

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.