The Maximum Diversity Problem calls for choosing $m$ items from a list of $n$ items, such that the diversity defined as some metric distance between items is maximized.
I have a simpler problem, which I was hoping I could solve in a simpler manner. In my case I have a list of $n$ items each with a certain non-unique key. I want to chose $m$ items from my list so that the maximal number of items per key is minimized.
e.g., if my list is:
('a', 5), ('b', 4), ('c', 2), ('a', 6), ('b', 5)
and we must choose $m=3$ items, an optimal solution would be a list containing one item for each key.
Is there an algorithm for doing this that is simpler than those for the Maximum Diversity Problem?