A malleable task is a computational unit which may be executed on any arbitrary number of processors, its execution time depending on the amount of resources allotted to it. According to the standard behavior of parallel applications, we assume that the malleable tasks are monotonic, i.e. that the execution time is decreasing with the number of processors while the computational work increases. This paper presents a new approach for scheduling a set of independent malleable tasks which leads to a worst case guarantee of fi for the minimization of the parallel execution time, or makespan. It improves all other existing practical results including the two-phases method introduced by Turek et al. The main idea is to transfer the difficulty of a two phases method from the scheduling part to the allotment selection. We show how to formulate this last problem as a knapsack optimization problem. Then, the scheduling problem is solved by a dual-approximation which leads to a simple structure of two consecutive shelves.
Mounie et. al. REF introduced malleable tasks that can use arbitrary numbers of processors and show monotonic behaviour, i.e. that the execution time decreases with increase of the number of processors.
Efficient approximation algorithms for scheduling malleable tasks
SPAA '99
Computer Science