A less obvious advantage of the n-ary indices is their ability to shed light into the local structure of large chemical spaces by singling out a molecule, or sampling a few species. The first of such applications that was explored in detail was the use of extended indices in diversity selection (e.g., selecting a maximally diverse subset from a given library). There are several ways to do this using binary comparisons (like the MaxMin and MaxSum algorithms), but they scale as O(N 2 ). On the other hand, with the extended similarity indices one can just directly maximize the diversity of the selected set by minimizing the extended similarity of the molecules that are going to be picked (e.g., the Max_nDis or ECS_MeDiv [136] algorithms). This simple procedure scales linearly, so it is in perfect position to handle very large datasets. Moreover, several benchmarks have shown that the Max_nDis algorithm can result in sets that are more than 3 times more diverse than those selected by MaxMin or MaxSum.