A Branch-and-Bound Algorithm For The Problem of Scheduling With a Conflict Graph

The problem of scheduling n unit-time jobs on m uniform machines is raised in this paper. The jobs are subject to conflicting constraints modeled by a graph G, called the conflict graph. Adjacent jobs (conflicting jobs) in G are not allowed to be processed on a same machine. The addressed objective is the minimization of the makespan of the schedule, which is known to be strongly NP-hard in the literature. The contribution of the current paper is an unorthodox branch-and-bound algorithm that proved to be highly efficient through empirical testing.