The problem of allocating task interaction graphs (TIGs) to heterogeneous computing systems to minimize job completion time is investigated. The only restriction is that the interprocessor communication cost is the same for any pair of processors. This is suitable for local area network based systems, such as Ethernet, as well as fully interconnected multiprocessor systems. An optimal polynomial solution exists if sufficient homogeneous processors and communication capacity are available. This solution is generalized to obtain two faster heuristics, one for the case of homogeneous processors and the other for heterogeneous processors. The heuristics were tested extensively with 60,900 systematically generated random TIGs and shown to be stable independent of the size of the TIG. A performance model is also proposed to predict the performance of the heuristic algorithms, and it is successful in explaining the experimental results qualitatively.
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