Multi processor scheduling algorithm for tasks with precedence relation

The problem of allocating and scheduling real-time tasks, with precedence constraints on multiprocessor architecture in order to meet the timing constraints is known to be NP complete. Due to the growing complexity of real-time applications there is a need to find scheduling methods that can handle large task sets in reasonable time. Also, scheduling methods should consider precedence and exclusion relations in order to support parallelism within tasks and to resolve mutual exclusion situations. Here we present an optimal non preemptive scheduling algorithm involving arbitrary precedence relations among tasks represented in the form of a DAG. We have shown here that a two phase algorithm is better than a single phase algorithm and also that our algorithm is better than the contemporary optimal algorithms in case of a two processor system and has polynomial time complexity.