Near-optimal dynamic task scheduling of precedence constrained coarse-grained tasks onto a computational grid

The most common objective function of task scheduling problems is makespan. However, on a computational grid, the 2nd optimal makespan may be much longer than the optimal makespan because the speed of each processor of a grid varies over time. So, if the performance measure is makespan, there is no approximation algorithm in general for scheduling onto a grid. In contrast, recently the authors proposed the computing power consumed by a schedule as a criterion of the schedule. For the criterion, this paper gives a (1 + Lcp(n)ċm(loge(m-1)+1)/n)-approximation algorithm for scheduling precedence constrained coarse-grained tasks with the same length onto a grid where n is the number of tasks, m is the number of processors, and Lcp(n) is the length of the critical path of the task graph. The proposed algorithm does not use any prediction information on the performance of underlying resources. Lcp(n) is usually a sublinear function of n. So, the above performance guarantee converges to one as n grows. This result implies a non-trivial result that the computing power consumed by an application on a grid can be limited within (1 + Lcp(n)ċm(loge(m-1)+1)/n) times that required by an optimal schedule in such a case.