Edge computing enables users to offload certain computation loads in complex applications to a nearby network consisting of multiple mobile devices such that the mobile devices’ resources can be integrated to afford these complex applications. Due to the social relationships among the owners of mobile devices, networks in edge computing are always complex and consist of multiple sub-networks intersecting at several joint devices. In such complex networks, a joint device can communicate with all devices belonging to all sub-networks that intersect at this joint device while a general device can only communicate with the devices belonging to the same sub-network. This paper studies the makespan-minimization workflow scheduling problem for the aforementioned complex networks in edge computing environments, and formulates the problem as an integer program. Due to the limited energy capacity of each device, the dependence among workflow tasks, as well as network complexity, it is challenging to achieve feasible scheduling solutions for the concerned problem. Therefore, we propose a family of task allocation strategies to cope with different types of tasks in the workflow. These strategies are further integrated with a greedy strategy to construct an improved greedy search (IGS) algorithm which is capable of generating feasible solutions satisfying all constraints. In addition, we propose an improved composite heuristic (ICH) algorithm that employs IGS to initialize a feasible solution and uses a two-layer improvement scheme to further enhance the quality of the initial solution. Simulation results show that our proposed IGS achieves an 100% probability of generating feasible solutions, as compared to a 2.3% probability achieved by using the general round-robin scheduling algorithm. Furthermore, IGS and ICH outperform the counterpart scheduling algorithms in terms of makespan reduction.

边缘计算使用户可以将复杂应用程序中的某些计算负载卸载到由多个移动设备组成的附近网络中，从而可以集成移动设备的资源以提供这些复杂应用程序。由于移动设备所有者之间的社会关系，边缘计算中的网络始终是复杂的，并且由在多个联合设备处相交的多个子网组成。在这样的复杂网络中，联合设备可以与属于在该联合设备处相交的所有子网的所有设备进行通信，而普通设备只能与属于同一子网的设备进行通信。本文研究了边缘计算环境中上述复杂网络的最小化工作流程调度问题，并将问题表述为整数程序。由于每个设备的能量容量有限，工作流程任务之间的依赖关系以及网络复杂性，对于相关问题实现可行的调度解决方案具有挑战性。因此，我们提出了一系列任务分配策略来应对工作流中不同类型的任务。这些策略进一步与贪婪策略集成在一起，以构建改进的贪婪搜索（IGS）算法，该算法能够生成满足所有约束的可行解决方案。此外，我们提出了一种改进的复合启发式算法（ICH），该算法采用IGS初始化可行的解决方案，并使用两层改进方案来进一步提高初始解决方案的质量。仿真结果表明，与使用常规轮询调度算法获得的2.3％的概率相比，我们提出的IGS可以实现产生可行解的概率为100％。此外，IGS和ICH在减少制造时间方面优于同类调度算法。