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Coflow is a recently proposed network abstraction to capture communicationpatterns in data centers. The coflow scheduling problem in large data centersis one of the most important $NP$-hard problems. Previous research on coflowscheduling focused mainly on the single-switch model. However, with recenttechnological developments, this single-core model is no longer sufficient.This paper considers the coflow scheduling problem in identical parallelnetworks. The identical parallel network is an architecture based on multiplenetwork cores running in parallel. Coflow can be considered as divisible orindivisible. Different flows in a divisible coflow can be transmitted throughdifferent network cores. Considering the divisible coflow scheduling problem,we propose a $(6-\frac{2}{m})$-approximation algorithm with arbitrary releasetimes, and a $(5-\frac{2}{m})$-approximation without release time, where $m$ isthe number of network cores. On the other hand, when coflow is indivisible, wepropose a $(4m+1)$-approximation algorithm with arbitrary release times, and a$(4m)$-approximation without release time.

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