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

An Algorithm for Reordering Buffer Management Problem and Experimental Evaluations on Discrete Distributions