English

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.

Keywords

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

R2 v1 2026-06-21T09:58:24.688Z