In a dedicated mixed-machine heterogeneous computing (HC) system, an application program may be decomposed into subtasks, then each subtask assigned to the machine where it is best suited for execution. Subtask data relocation is defined as selecting the sources for their needed data items. This study focuses on theoretical issues for data relocation using a stochastic HC model. It is assumed that multiple independent subtasks of an application program can be executed concurrently on different machines whenever possible. A stochastic model for HC is proposed, in which the computation times of subtasks and communication times for inter-machine data transfers can be random variables. The optimization problem for finding the optimal matching, scheduling, and data relocation schemes to minimize the total execution time of an application program is defined based on this stochastic HC model. The optimization criteria and search space for the above optimization problem are described. It is proven that a greedy algorithm based approach will generate the optimal data relocation scheme with respect to any fixed matching and scheduling schemes. This result indicates that a greedy algorithm based approach is the best strategy for developing data relocation heuristics in practice.
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