TL;DR
This paper proves that the binary coin set is optimal for minimizing the number of coins needed for any change-making transaction and has the best asymptotic average cost among all completely greedy coin sets.
Contribution
It establishes the optimality of the binary coin set in the context of completely greedy coin systems for change-making.
Findings
Binary coin set minimizes coins needed for any transaction.
Asymptotic average cost of binary set is optimal among greedy sets.
Binary set outperforms other greedy coin sets in efficiency.
Abstract
We show that the binary coin set minimizes the number of coins needed to guarantee the ability to make change in any one transaction and its asymptotic uniform average cost is no worse than that of any completely greedy coin set.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Limits and Structures in Graph Theory