In data-parallel computing frameworks, intermediate
parallel data is often produced at various stages which
needs to be transferred among servers in the datacenter network (e.g. the shuffle phase in MapReduce). A stage often cannot start or be completed unless all the required data pieces from the preceding stage are received. Coflow is a recently proposed networking abstraction to capture such communication patterns. We consider the problem of efficiently scheduling coflows with release dates in a shared datacenter network so as to minimize the total weighted completion time of coflows. Our main result is a polynomial-time algorithm that improves the prior known approximation results. Specifically, we propose a deterministic algorithm with approximation ratio of 5, which improves the prior best known ratio of 12. For the special case when all coflows are released at time zero, our algorithm obtains approximation ratio of 4 which improves the prior best known ratio of 8. Extensive simulation results, using both synthetic and real traffic traces, are presented that verify the performance of our algorithm and show improvement over the prior approaches.