Data Partitioning with a Functional Performance Model of Heterogeneous Processors

In this paper, we address the problem of optimal distribution of computational tasks on a network of heterogeneous computers when one or more tasks do not fit into the main memory of the processors and when relative speeds vary with the problem size. We propose a functional performance model of heterogeneous processors that integrates many essential features of a network of heterogeneous computers having a major impact on its performance such as the processor heterogeneity, the heterogeneity of memory structure, and the effects of paging. Under this model, the speed of each processor is represented by a continuous function of the size of the problem whereas traditional models use single numbers to represent the speeds of the processors. We formulate a problem of partitioning of an nelement set over p heterogeneous processors using this model and design an algorithm of the complexity O(p × log2n) solving the problem.