Characterization of canonical systems with six types of coins for the change-making problem

Autor:	Suzuki, Yuma, Miyashiro, Ryuhei
Rok vydání:	2021
Předmět:	Computer Science - Discrete Mathematics 68Q25 68R05 90C10 F.2.2 G.2.1
Druh dokumentu:	Working Paper
Popis:	This paper analyzes a necessary and sufficient condition for the change-making problem to be solvable with a greedy algorithm. The change-making problem is to minimize the number of coins used to pay a given value in a specified currency system. This problem is NP-hard, and therefore the greedy algorithm does not always yield an optimal solution. Yet for almost all real currency systems, the greedy algorithm outputs an optimal solution. A currency system for which the greedy algorithm returns an optimal solution for any value of payment is called a canonical system. Canonical systems with at most five types of coins have been characterized in previous studies. In this paper, we give characterization of canonical systems with six types of coins, and we propose a partial generalization of characterization of canonical systems. Comment: 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.12392 Zobrazit plný text záznamu View this record from Arxiv