Combinatorics of the change-making problem
Combinatorics
2010-07-26 v2
Abstract
We investigate the structure of the currencies (systems of coins) for which the greedy change-making algorithm always finds an optimal solution (that is, a one with minimum number of coins). We present a series of necessary conditions that must be satisfied by the values of coins in such systems. We also uncover some relations between such currencies and their sub-currencies.
Cite
@article{arxiv.0801.0120,
title = {Combinatorics of the change-making problem},
author = {Michal Adamaszek and Anna Niewiarowska},
journal= {arXiv preprint arXiv:0801.0120},
year = {2010}
}
Comments
18 pages, 4 figures Added a partial proof of conjecture 7.6 + some minor changes