Initially, matroids were introduced to generalize the notions of linear independence of a collection of subsets $E$ over some ground set $I$. Certain problems that contain this structure permit greedy algorithms to find optimal solutions. The concept of greedoids was later introduced to generalize this structure to capture more problems that allow for optimal solutions to be found by greedy methods.
How often do these structures arise in algorithm design?
Furthermore, more often than not a greedy algorithm will not be able to fully capture what is necessary to find optimal solutions, but may still find very good approximate solutions (Bin Packing, for example). Given that, is there a way to measure how "close" a problem is to a greedoid or matroid?