TASK-SCHEDULING WITH PRECEDENCE CONSTRAINTS TO MINIMIZE THE TOTAL COMPLETION-TIME

The authors study the problem of scheduling a set of tasks with known execution times and arbitrary precedence constraints to computing systems. The objective function used to measure the performance of a schedule in this paper is the sum of completion times of all tasks, which is called total completion time. Finding the minimum total completion time of tasks with precedence constraints on the uniprocessor system is known to be NP-complete, let alone on the multiprocessor system (Garey and Johnson 1979). Based on the well-known A* algorithm proposed in the field of artificial intelligence (Nilson 1980), two algorithms are developed to solve efficiently the scheduling problems on the uniprocessor system and multiprocessor system. Some evaluation functions are proposed to accelerate the search of an optimal schedule. A table named the backwards range-limited table is used to assist the computation of the evaluation function. Experimental results show that the proposed approaches can achieve the optimal schedule with greatly reduced search tree size, especially when bounding rules are applied.