We consider routing in reconfigurable networks, which is also known as coflow scheduling in the literature. The algorithmic literature generally (perhaps implicitly) assumes that the amount of data to be transferred is large. Thus the standard way to model a collection of requested data transfers is by an integer demand matrix $D$, where the entry in row $i$ and column $j$ of $D$ is an integer representing the amount of information that the application wants to send from machine/node $i$ to machine/node $j$. A feasible coflow schedule is then a sequence of matchings, which represent the sequence of data transfers that covers $D$. In this work, we investigate coflow scheduling when the size of some of the requested data transfers may be small relative to the amount of data that can be transferred in one round. fractional matchings and/or that employ indirect routing, and compare the relative utility of these options. We design algorithms that perform much better for small demands than the algorithms in the literature that were designed for large data transfers.

翻译：本文研究可重构网络中的路由问题，该问题在文献中亦称为协同流调度。算法研究领域通常（可能隐含地）假设待传输数据量较大，因此对请求数据传输集合的标准建模方式是采用整数需求矩阵$D$，其中$D$第$i$行第$j$列的元素为整数，表示应用程序期望从机器/节点$i$发送至机器/节点$j$的信息量。可行的协同流调度即为一系列匹配的序列，这些匹配构成的传输序列需覆盖$D$。本研究探讨当部分请求数据传输规模相对于单轮可传输数据量较小时的协同流调度问题。我们提出允许分数匹配和/或采用间接路由的调度方案，并比较这些方案的相对效用。针对小规模需求场景，我们设计的算法性能显著优于文献中为大规模数据传输设计的算法。