Minimizing sum of completion times and makespan in master-slave systems

We consider scheduling problems in the master-slave model. In this model, each job has to be processed sequentially in three stages. In the first stage, a preprocessing task runs on a master machine, in the second stage, a slave task runs on a dedicated slave machine, and, in the last stage, a postprocessing task again runs on a master machine, possibly different from the master machine in the first stage. It has been shown that the problem of minimizing the makespan or the sum of completion times is NP-hard in the strong sense even if preemption is allowed. In this paper, we design efficient approximation algorithms to minimize the sum of completion times in various settings. These are the first general results for the minsum problem in the master-slave model. We also show that these algorithms generate schedules with small makespan as well