Exact algorithms for scheduling programs with shared tasks

We study a scheduling problem where the jobs we have to perform are composed of one or more tasks. If two jobs sharing a non-empty subset of tasks are scheduled on the same machine, then these shared tasks have to be performed only once. This kind of problem is known in the literature under the names of VM-PACKING or PAGINATION. Our objective is to schedule a set of these objects on two parallel identical machines, with the aim of minimizing the makespan. This problem is NP-complete as an extension of the PARTITION problem. In this paper we present three exact algorithms with worst-case time-complexity guarantees, by exploring different branching techniques. Our first algorithm focuses on the relation between jobs sharing one or more symbols in common, whereas the two other algorithms branches on the shared symbols.