An approximation algorithm for scheduling dependent tasks on m processors with small communication delays

This paper de nes and studies an approximation algorithm for scheduling tasks with small communication delays onm processors. In a rst step, a schedule 1 for the problem instance with an unlimited number of processors is generated with a polynomial algorithm with relative performance bounded by 2(1 + ) 2 + , where denotes the ratio between the greatest communication delay and the smallest processing time. Then this solution is used to solve the resource con icts during the scheduling phase on m processors, with a rather unusual feature: a processor may remain idle even if some tasks are feasible in order to wait for a more important task. The schedule generated by this algorithm is proved to have an overall worst case performance 4 + 3 2 + 2 + 2 (2 + )m , improving the best known ratio 2 + 2 m .