  With the rapid advancement of technology, parallel computing applications
have become increasingly popular and are commonly executed in large data
centers. These applications involve two phases: computation and communication,
which are executed repeatedly to complete the work. However, due to the
ever-increasing demand for computing power, large data centers are struggling
to meet the massive communication demands. To address this problem, coflow has
been proposed as a networking abstraction that captures communication patterns
in data-parallel computing frameworks. This paper focuses on the coflow
scheduling problem in identical parallel networks, where the primary objective
is to minimize the makespan, which is the maximum completion time of coflows.
It is considered one of the most significant $\mathcal{NP}$-hard problems in
large data centers. In this paper, we consider two problems: flow-level
scheduling and coflow-level scheduling. In the flow-level scheduling problem,
distinct flows can be transferred through different network cores, whereas in
the coflow-level scheduling problem, all flows must be transferred through the
same network core. To address the flow-level scheduling problem, this paper
proposes two algorithms: a $(3-\tfrac{2}{m})$-approximation algorithm and a
$(\tfrac{8}{3}-\tfrac{2}{3m})$-approximation algorithm, where $m$ represents
the number of network cores. For the coflow-level scheduling problem, this
paper proposes a $(2m)$-approximation algorithm. Finally, we conduct
simulations on our proposed algorithm and Weaver's algorithm, as presented in
Huang \textit{et al.} (2020) in the 2020 IEEE International Parallel and
Distributed Processing Symposium (IPDPS). We also validate the effectiveness of
the proposed algorithms on heterogeneous parallel networks.
