  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.
