In the reordering buffer management problem, a sequence of requests must be executed by a service station, where a cost occurs for each pair of consecutive requests with different attributes. A reordering buffer management algorithm aims to permute the input sequence using the buffer to minimize the total cost. Reordering buffers has many potential applications in computer sciences and economics. In this article, we proved the minimum buffer length for the optimal solution to the reordering buffer management problem in the offline setting. With the assumption that color selection is always made when the buffer is full, selecting the most frequent color from the buffer given the smallest buffer size $k$ that satisfies either $o_1 < 2 \cdot \lceil \frac{k}{\sigma} \rceil$ OR $o_2 < \lceil \frac{k}{\sigma} \rceil$ guarantees the optimal solution, where $o_1$ and $o_2$ represent respectively the frequency of the most and the second most frequent colors in the input sequence $\mathcal{X}$, and $\sigma$ is the number of distinct colors appearing in $\mathcal{X}$. We proposed a new algorithm for the online setting of the problem that uses the results of the proof made on the minimum buffer length required for the optimal solution. Moreover, we presented the results of the first experimental setup that uses input sequences following discrete distributions to evaluate the performance of algorithms. Out of 432 cases, the new algorithm showed the best performance in 409 cases that is approximately $95\%$ of all cases.

翻译：在重新排序缓冲管理问题中,请求的顺序必须由一个服务站执行,因为每对具有不同属性的连续请求每对相继请求都有成本。 重新排序缓冲管理算法的目的是使用缓冲来调整输入序列以尽量减少总成本。 重新排序缓冲在计算机科学和经济学中有许多潜在应用。 在本篇文章中, 我们证明了最理想解决离线设置中重新排序缓冲管理问题的最佳办法的最小缓冲长度。 假设在缓冲完全时总是进行色选择, 从缓冲中选择最经常的颜色, 最小的缓冲大小为 $1 < 1 < 2\ cdot\ lceil\ frac{ kuns gma}\\ rice$2 < or or_ 2 <\ clcel{kunsgma}\ rice gree$2 。 提出最优化解决方案的频率为$1美元和$2$。 在最小的缓冲序列中, 最经常的颜色为美元=美元=xxx美元。 在最短的缓冲序列中, 我们最起码的递增的递解的递增的递增的递解算结果显示了 4xxx。