  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.
