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Biobjective optimization problems on matroids with binary costs
Published in Optimization, 2023
Jochen Gorski, Kathrin Klamroth, Julia Sudhoff
Given a matroid , a basis and an element , then contains a uniquely determined circuit containing e. This circuit is also called the fundamental circuit of e w.r.t. B. An important property of matroids is the basis exchange property:
The following stronger version of the basis exchange property was proven in [32].
Input matrix construction and approximation using a graphic approach
Published in International Journal of Control, 2020
Yuan Zhang, Tong Zhou
Matroids are combinatorial structures that abstract the notion of linear independence in vector spaces. A matroid is a pair where E is a finite ground set, and is the family of subsets of E which are said to be the independent sets. For notion of matroids, readers can refer to Lawler (1975), Murota (2009).