Solving hard real-time scheduling problems on a single processor

Many applications e.g. from operations research, or areas like operating systems or control systems, deal with sets of activities or tasks that are of real time character, i.e. certain deadlines have to be obeyed in order to guarantee the correct function of the application. In scheduling theory, algorithms are developed with-depending on the particular requirements of the application-the objective to sequence given sets of tasks feasibly, or to minimize the number of tardy tasks. Results obtained in this area show that finding an optimal solution is NP hard in most cases. An exact method called the SIT graph approach is presented that, though its time complexity increases exponentially with the number of tasks, allows one to solve interesting and practically important classes of scheduling problems in polynomial time. This method is used for scheduling sets of hard real time tasks on a single machine.