Maximum-Weight Matroid Optimisation Problem

Definition

Maximum-Weight Matroid Optimisation Problem

The Maximum-Weight Matroid Optimisation Problem is a matroid optimisation problem in which, given a matroid $M=(E,\mathcal{I})$ and a weight function

$$\omega :E\to \mathbb{N},$$

the goal is to find an independent set $I^{\ast }\in \mathcal{I}$ of maximum total weight:

$$I^{\ast }\in \arg \underset{I\in \mathcal{I}}{\max }\omega (I),\text{where}\omega (I)=\sum _{e\in I}\omega (e).$$