The deployment of cloud and edge computing forms a three-tier mobile computing network, where each task can be processed locally, by the edge nodes, or by the remote cloud server. In this paper, we consider a cooperative three-tier computing network by leveraging the vertical cooperation among devices, edge nodes and cloud servers, as well as the horizontal cooperation between edge nodes. In this network, we jointly optimize the offloading decision and the computation resource allocation to minimize the average task duration subject to the limited battery capacity of devices. However, the formulated problem is a large-scale mixed integer non-linear optimization problem with the growing number of base stations and devices,which is NP-hard in general. To develop an efficient offloading scheme with low complexity, we conduct a series of reformulation based on reformulation linearization technology (RLT) and further propose a parallel optimization framework by utilizing alternating direction method of multipliers (ADMM) method and difference of convex functions (D.C.) programming. The proposed scheme decomposes the large-scale problem into some smaller sub problems, which are done across the multiple computation units in a parallel fashion to speed up the computation process.Simulation results demonstrate that the proposed scheme can obtain a near-optimal performance with low complexity, and can reduce up to 24% of the task duration compared with other schemes. Simulation also shows how much the vertical and horizontal computation cooperations affect the system performanceunder different network parameters.
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