Coin selection refers to the problem of choosing a set of tokens to fund a transaction in token-based payment systems such as, e.g., cryptocurrencies or central bank digital currencies (CBDCs). In this paper, we propose the Boltzmann Draw that is a probabilistic algorithm inspired by the principles of statistical physics. The algorithm relies on drawing tokens according to the Boltzmann distribution, serving as an extension and improvement of the Random Draw method. Numerical results demonstrate the effectiveness of our method in bounding the number of selected input tokens as well as reducing dust generation and limiting the token pool size in the wallet. Moreover, the probabilistic algorithm can be implemented efficiently, improves performance and respects privacy requirements - properties of significant relevance for current token-based technologies. We compare the Boltzmann draw to both the standard Random Draw and the Greedy algorithm. We argue that the former is superior to the latter in the sense of the above objectives. Our findings are relevant for token-based technologies, and are also of interest for CBDCs, which as a legal tender possibly needs to handle large transaction volumes at a high frequency.

翻译：硬币选择指的是在基于代币的支付系统（例如加密货币或中央银行数字货币）中选择一组代币为交易提供资金的问题。本文提出一种受统计物理学原理启发的概率算法——玻尔兹曼抽取法。该算法依据玻尔兹曼分布抽取代币，是对随机抽取法的扩展与改进。数值结果表明，我们的方法能有效限制所选输入代币的数量、减少粉尘生成并控制钱包中的代币池规模。此外，该概率算法可实现高效执行，在提升性能的同时满足隐私保护要求——这些特性对当前基于代币的技术具有重要意义。我们将玻尔兹曼抽取法与标准随机抽取法及贪心算法进行比较，论证了前者在上述目标维度上优于后者。本研究对基于代币的技术具有参考价值，对可能需要高频处理大规模交易量的法定数字货币同样具有借鉴意义。