In this paper we focus on the problem of data aggregation using two aggregators in a data center network, where the source racks are allowed to split their data and send to the aggregators using multiple paths. We show that the problem of finding a topology that minimizes aggregation time is NP-hard for k = 2, 3, 4, where k is the maximum degree of each ToR switch (number of uplinks in a top-of-rack switch) in the data center. We also show that the problem becomes solvable in polynomial time for k = 5 and 6 and conjecture the same for k $>$> 6. Experimental results show that, for k = 6, our topology optimization algorithm reduces the aggregation time by as much as 83.32 percent and reduces total network traffic by as much as 99.5 percent relative to the torus heuristic, proposed in [1] , which readily proves the significant improvement in performance achieved by the proposed algorithm.

中文翻译：

---

在数据中心网络中使用多条路径的双聚合器拓扑优化

在本文中，我们关注在数据中心网络中使用两个聚合器进行数据聚合的问题，其中允许源机架拆分其数据并使用多条路径发送到聚合器。我们表明，对于 k = 2, 3, 4，找到最小化聚合时间的拓扑是 NP-hard 问题，其中 k 是每个 ToR 交换机的最大程度（架顶交换机中的上行链路数量）数据中心。我们还表明，对于 k = 5 和 6，问题在多项式时间内变得可解，并且对 k 的猜想也是如此$>$> 6. 实验结果表明，对于 k = 6，我们的拓扑优化算法将聚合时间减少了 83.32%，并且相对于环面启发式算法减少了 99.5% 的总网络流量。 [1] ，这很容易证明所提出的算法所实现的性能显着提高。