Applications designed for data-parallel computation frameworks such as MapReduce usually alternate between computation and communication stages. Coflow scheduling is a recent popular networking abstraction introduced to capture such application-level communication patterns in datacenters. In this framework, a datacenter is modeled as a single non-blocking switch with m input ports and m output ports. A coflow j is a collection of flow demands {d_(io)~j}i∈m,o∈m that is said to be complete once all of its requisite flows have been scheduled. We consider the offline coflow scheduling problem with and without release times to minimize the total weighted completion time. Coflow scheduling generalizes the well studied concurrent open shop scheduling problem and is thus NP-hard. Qiu, Stein and Zhong [15] obtain the first constant approximation algorithms for this problem via LP rounding and give a deterministic 67/3-approximation and a randomized (9 + 16{the square root of}2/3) ≈ 16.54-approximation algorithm. In this paper, we give a combinatorial algorithm that yields a deterministic 5-approximation algorithm with release times, and a deterministic 4-approximation for the case without release time.
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