Given a cycle graph of n nodes and a non-negative demand $d_{i,j}$ for each pair of nodes $i,j$, the ring loading problem with demand splitting (RLPW) asks to determine a routing of these demands such that the maximum load on any edge is minimal. In this work, we present an algorithm for computing minimal solutions to RLPW in $\mathcal{O}(n^2)$ time. This algorithm, when employed as a subroutine, also improves the runtimes for several other ring loading algorithms by a factor of up to $\mathcal{O}(n^2)$.

中文翻译：

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计算环加载问题的最小解

给定一个包含n 个节点的循环图和一个非负需求$d_{我,j}$对于每对节点$我,j$，具有需求分割（RLPW）的环负载问题要求确定这些需求的路由，使得任何边缘上的最大负载最小。在这项工作中，我们提出了一种计算RLPW最小解的算法$\mathcal{氧}（n^2）$时间。该算法当用作子程序时，还可以将其他几种环加载算法的运行时间提高多达一个因子$\mathcal{氧}（n^2）$。