The Reconfigurable Routing Problem (RRP) in hybrid networks is, in short, the problem of finding settings for optical switches augmenting a static network so as to achieve optimal delivery of some given workload. The problem has previously been studied in various scenarios with both tractable and NP-hardness results obtained. However, the data center and interconnection networks to which the problem is most relevant are almost always such that the static network is highly structured whereas all previous results assume that the static network can be arbitrary (which makes existing computational hardness results less technologically relevant and also easier to obtain). In this paper, and for the first time, we prove various intractability results for RRP where the underlying static network is highly structured, for example consisting of a hypercube, and also extend some existing tractability results.

翻译：可重构路由问题（RRP）在混合网络中的核心任务可概括为：为增强静态网络的光学交换机寻找最优配置，以实现指定工作负载的高效传输。该问题此前已在多种场景下得到研究，并获得了可解性与NP难度性结论。然而，与该问题最相关的数据中心及互连网络往往具有高度结构化的静态网络特性，而此前所有研究均假设静态网络可以是任意形态（这使得现有计算复杂性结论的技术相关性降低，且更易获得）。本文首次针对底层静态网络具有高度结构化特征（例如由超立方体构成）的RRP场景，证明了多种难解性结果，并扩展了部分现有的可解性结论。