Scheduling Coflows for Minimizing the Total Weighted Completion Time in Heterogeneous Parallel Networks

Coflow is a network abstraction used to represent communication patterns in data centers. The coflow scheduling problem in large data centers is one of the most important $NP$-hard problems. Many previous studies on coflow scheduling mainly focus on the single-core model. However, with the growth of data centers, this single-core model is no longer sufficient. This paper considers the coflow scheduling problem in heterogeneous parallel networks. The heterogeneous parallel network is an architecture based on multiple network cores running in parallel. In this paper, two polynomial-time approximation algorithms are developed for scheduling divisible and indivisible coflows in heterogeneous parallel networks, respectively. Considering the divisible coflow scheduling problem, the proposed algorithm achieve an approximation ratio of $O(\log m/ \log \log m)$ with arbitrary release times, where $m$ is the number of network cores. On the other hand, when coflow is indivisible, the proposed algorithm achieve an approximation ratio of $O\left(m\left(\log m/ \log \log m\right)^2\right)$ with arbitrary release times.