Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and routing in such demand-aware networks to minimize congestion, along two dimensions: (1) splittable or unsplittable flows, and (2) whether routing is segregated, i.e., whether routes can or cannot combine both demand-aware and demand-oblivious (static) links. For splittable and segregated routing, we show that the problem is generally $2$-approximable, but APX-hard even for uniform demands induced by a bipartite demand graph. For unsplittable and segregated routing, we establish upper and lower bounds of $O\left(\log m/ \log\log m \right)$ and $\Omega\left(\log m/ \log\log m \right)$, respectively, for polynomial-time approximation algorithms, where $m$ is the number of static links. We further reveal that under un-/splittable and non-segregated routing, even for demands of a single source (resp., destination), the problem cannot be approximated better than $\Omega\left(\frac{c_{\max}}{c_{\min}} \right)$ unless P=NP, where $c_{\max}$ (resp., $c_{\min}$) denotes the maximum (resp., minimum) capacity. It remains NP-hard for uniform capacities, but is tractable for a single commodity and uniform capacities. Our trace-driven simulations show a significant reduction in network congestion compared to existing solutions.

翻译：新兴的可重构光通信技术允许通过针对流量模式优化的需求感知链路来增强数据中心拓扑结构。本文研究了在此类需求感知网络中联合优化拓扑和路由以最小化拥塞的算法问题，涉及两个维度：（1）可分割或不可分割的流，（2）路由是否分离，即路由是否可以同时结合需求感知链路和需求 oblivious（静态）链路。对于可分割且分离的路由，我们证明该问题通常可实现$2$倍近似，但即使对于由二分需求图诱导的均匀需求，也是APX难的。对于不可分割且分离的路由，我们分别建立了多项式时间近似算法的上界和下界，为$O\left(\log m/ \log\log m \right)$和$\Omega\left(\log m/ \log\log m \right)$，其中$m$是静态链路的数量。我们进一步揭示，在不可分割/可分割且非分离的路由下，即使对于单一源（或目的地）的需求，除非P=NP，否则该问题的近似比不能优于$\Omega\left(\frac{c_{\max}}{c_{\min}} \right)$，其中$c_{\max}$（或$c_{\min}$）表示最大（或最小）容量。对于均匀容量，该问题仍然是NP难的，但对于单一商品和均匀容量则是可处理的。我们的基于实际流量的仿真结果显示，与现有解决方案相比，网络拥塞显著减少。