Some important special cases of matroid-constrainted partitioning problems are:[1] General matroid constraints were first considered by Burkard and Yao.
Hwang and Rothblum[3] presented an alternative sufficient condition.
Wu and Yao[4] presented an approximation algorithm for minimizing (max,sum) with general matroid constraints.
Abbassi, Mirrokni and Thakur[5] present an approximation algorithm for a problem of diversity maximization under matroid constraints.
There is a single matroid, and the goal is to partition its elements into a smallest number of independent sets.