With the development of technology, parallel computing applications have been commonly executed in large data centers. These parallel computing applications include the computation phase and communication phase, and work is completed by repeatedly executing these two phases. However, due to the ever-increasing computing demands, large data centers are burdened with massive communication demands. Coflow is a recently proposed networking abstraction to capture communication patterns in data-parallel computing frameworks. This paper focuses on the coflow scheduling problem in identical parallel networks, where the goal is to minimize makespan, the maximum completion time of coflows. The coflow scheduling problem in huge data center is considered one of the most significant $NP$-hard problems. In this paper, coflow can be considered as either a divisible or an indivisible case. Distinct flows in a divisible coflow can be transferred through different network cores, while those in an indivisible coflow can only be transferred through the same network core. In the divisible coflow scheduling problem, this paper proposes a $(3-\tfrac{2}{m})$-approximation algorithm, and a $(\tfrac{8}{3}-\tfrac{2}{3m})$-approximation algorithm, where $m$ is the number of network cores. In the indivisible coflow scheduling problem, this paper proposes a $(2m)$-approximation algorithm. Finally, we simulate our proposed algorithm and Weaver's [Huang \textit{et al.}, In 2020 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pages 1071-1081, 2020.] and compare the performance of our algorithms with that of Weaver's.

翻译：随着技术的发展，并行计算应用已在大型数据中心广泛部署。这类应用包含计算阶段与通信阶段，通过反复执行这两个阶段完成任务。然而，由于计算需求的持续增长，大型数据中心面临巨大的通信负载压力。Coflow是近期提出的网络抽象概念，用于捕获数据并行计算框架中的通信模式。本文聚焦同质并行网络中的coflow调度问题，目标是最小化最大完成时间（makespan）。在超大规模数据中心中，coflow调度问题被认为是最重要的NP难问题之一。本文将coflow分为可分割与不可分割两种情形：可分割coflow中的不同流可通过不同网络核心传输，而不可分割coflow中的流只能通过同一网络核心传输。针对可分割coflow调度问题，本文提出了(3-2/m)近似算法和(8/3-2/(3m))近似算法（其中m为网络核心数）；针对不可分割coflow调度问题，提出了(2m)近似算法。最后，我们通过仿真实验将所提算法与Weaver算法[Huang et al., 2020 IEEE国际并行与分布式处理研讨会(IPDPS), 第1071-1081页, 2020]进行性能对比。