Scheduling on hierarchical clusters using malleable tasks

The model of malleable task (MT) was introduced some years ago and has been proved to be an efficient way for implementing parallel applications. It considers a target application at a larger level of granularity than in other models (corresponding typically to numerical routines) where the tasks can themselves be executed in parallel. Clusters of SMP (symmetric Multi-Processors) are a cost effective alternative to parallel supercomputers. Such hierarchical clusters are parallel systems made from m SMP composed each by k identical processors. They are more and more popular, however, designing efficient software that take full advantage of such systems remains difficult. This work describes a 2-2/k approximation algorithm for scheduling a set of independent malleable tasks for the minimization of the parallel execution time, where $k$ is a power of 2 (k > 2). For k=2, a special treatment leads to the bound of 3/2 which is the best known for non hierarchical tasks. The algorithm presented here is a fully polynomial approximation scheme running in O(nmk) time