A multiply constrained matroid optimization problem

The authors consider the problem of finding a minimum weight basis in a matroid satisfying additional conditions which can be described as follows: each element of the matroid is assigned a colour and feasible bases can use at most a prescribed number of elements from each colour. This problem is a special case of weighted matroid intersection. The authors provide an algorithm for this problem which improves general matroid intersection algorithms by exploiting the simple structure of the side constraints.