In a heterogeneous computing (HC) environment consisting of different types of machines, an application program is decomposed into subtasks, each of which is computationally homogeneous. The goal is to execute subtasks on the machines in such a way that the total program execution time is minimized. A mathematical framework is presented that models the matching of subtasks to machines, scheduling of subtasks' computation, scheduling of intermachine communication steps, and selection of sources of shared data items for intermachine communication (data relocation). The goal of this work is to generate a provably optimal scheme for communicating shared data among subtasks as an enhancement to any given matching and scheduling. Initially, it is assumed that at any instant in time, only one machine is being used for program execution and only one subtask is being executed. Based on this assumption, a polynomial algorithm is introduced to optimize scheduling and data relocation with respect to any given matching of subtasks to machines. The data relocation scheme is then extended to reduce intermachine data communication time in an HC environment with a given matching and scheduling of subtasks' computation where: multiple subtasks' computations can be performed concurrently on different machines; subtask computation steps can be overlapped with other subtasks' communication steps for intermachine data transfers; and machines in the HC suite are interconnected by a shared-bus type of network.