Task spreading and shrinking on multiprocessor systems and networks of workstations

In this paper, we describe how our computational model can be used for the problems of processor allocation and task mapping. The intended applications for this model include the dynamic mapping problems of shrinking or spreading an existing mapping when the available pool of processors changes during execution of the problem. The concept of problem edge class and other features of our model are developed to realistically and efficiently support task partitioning and merging for static and dynamic mapping. The model dictates realistic changes in the computation and communication characteristics of a problem when the problem partitioning is modified dynamically. This model forms the basis of our algorithms for shrinking and spreading, and yields realistic results for a variety of problems mapped onto real systems. An emulation program running on a network of workstations under PVM is used to measure execution times for the mapping solutions found by the algorithms. The results indicate that the problem edge class is a crucial consideration for processor allocation and task mapping.