Scheduling with agreements: new results

In this paper, the problem of scheduling with agreements (SWA) is considered. In scheduling, this consists of a set of jobs non-preemptively on identical machines subject to constraints that only some specific jobs can be scheduled concurrently on different machines. These constraints are given by an agreement graph and the aim is to minimise the makespan. In the case of two machines we extend two NP-hardness results of SWA with processing times at most three that hold for bipartite agreement graphs to more general agreement graphs. Complexity results of SWA are established in the case of split and complement of bipartite graphs. We also present some approximation results for SWA.