Efficient Approximation Algorithms for Scheduling Coflows With Total Weighted Completion Time in Identical Parallel Networks

This article addresses the scheduling problem of coflows in identical parallel networks, a well-known $\mathcal {NP}$ -hard problem. We consider both flow-level scheduling and coflow-level scheduling problems. In the flow-level scheduling problem, flows within a coflow can be transmitted through different network cores, while in the coflow-level scheduling problem, flows within a coflow must be transmitted through the same network core. The key difference between these two problems lies in their scheduling granularity. Previous approaches relied on linear programming to solve the scheduling order. In this article, we enhance the efficiency of solving by utilizing the primal-dual method. For the flow-level scheduling problem, we propose an approximation algorithm that achieves approximation ratios of $6-\frac{2}{m}$ and $5-\frac{2}{m}$ for arbitrary and zero release times, respectively, where $m$ represents the number of network cores. Additionally, for the coflow-level scheduling problem, we introduce an approximation algorithm that achieves approximation ratios of $4m+1$ and $\text{4}m$ for arbitrary and zero release times, respectively. The algorithm presented in this article has practical applications in data centers, such as those operated by Google or Facebook. The simulated results demonstrate the superior performance of our algorithms compared to previous approach, emphasizing their practical utility.