  Coflow is a recently proposed network abstraction for data-parallel computing
applications. This paper considers scheduling coflows with precedence
constraints in identical parallel networks, such as to minimize the total
weighted completion time of coflows. The identical parallel network is an
architecture based on multiple network cores running in parallel. In the
divisible coflow scheduling problem, the proposed algorithm achieves
$(6-\frac{2}{m})\mu$ and $(5-\frac{2}{m})\mu$ approximate ratios for arbitrary
release time and zero release time, respectively, where $m$ is the number of
network cores and $\mu$ is the coflow number of the longest path in the
precedence graph. In the indivisible coflow scheduling problem, the proposed
algorithm achieves $(4m+1)\mu$ and $4m\mu$ approximate ratios for arbitrary
release time and zero release time, respectively. In the single network core
scheduling problem, we propose a $5\mu$-approximation algorithm with arbitrary
release times, and a $4\mu$-approximation without release time. Moreover, the
proposed algorithm can be modified to solve the coflows of multi-stage jobs
scheduling problem. In multi-stage jobs, coflow is transferred between servers
to enable starting of next stage. This means that there are precedence
constraints between coflows of job. Our result represents an improvement upon
the previous best approximation ratio of $O(\tilde{\mu} \log(N)/
\log(\log(N)))$ where $\tilde{\mu}$ is the maximum number of coflows in a job
and $N$ is the number of servers.
