Consider a set of jobs connected to a directed acyclic task graph with a fixed source and sink. The edges of this graph model precedence constraints and the jobs have to be scheduled with respect to those. We introduce the Server Cloud Scheduling problem, in which the jobs have to be processed either on a single local machine or on one of many cloud machines. Both the source and the sink have to be scheduled on the local machine. For each job, processing times both on the server and in the cloud are given. Furthermore, for each edge in the task graph, a communication delay is included in the input and has to be taken into account if one of the two jobs is scheduled on the server, the other in the cloud. The server can process jobs sequentially, whereas the cloud can serve as many as needed in parallel, but induces costs. We consider both makespan and cost minimization. The main results are an FPTAS with respect for the makespan objective for a fairly general case and strong hardness for the case with unit processing times and delays.

翻译：考虑一组作业，它们连接到一个具有固定源点和汇点的有向无环任务图。该图的边模拟了作业之间的优先约束关系，且作业必须遵循这些约束进行调度。我们提出了服务器云计算调度问题，其中作业必须在单个本地机器或众多云机器中的一台进行处理。源点和汇点均需调度在本地机器上。对于每个作业，服务器和云计算的处理时间均已给定。此外，任务图中的每条边，输入中包含了通信延迟，若一个作业调度在服务器上、另一个在云中，则需考虑该延迟。服务器可顺序处理作业，而云则能以并行方式处理任意数量作业，但会产生成本。我们同时考虑完工时间和成本的最小化。主要结果包括：针对一个相当一般的情况，在完工时间目标下给出一个全多项式时间近似方案（FPTAS）；而对于单位处理时间和延迟的情况，证明了强困难性。