Algorithm to find optimal currency denominations
This is related to the well-known change-making problem. So well-studied, in fact, that this question has been investigated for $m \leq 7$ [1] using brute force. As of 2003, the hardness of finding optimal denominations appears to be an open problem.

If you check the articles citing Shallit, it seems as if denominations enabling greedy change-making strategies were of particular interest. It is clear that such denominations have advantages in practice.




What This Country Needs is an 18c Piece
 by Jeffrey Shallit (2003)