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A recently published algorithm shows how to assign modules to a two-processor computer system with distributed execution so as to minimize the total of execution costs and interprocessor communication costs. In this paper we consider the same problem except that one processor has limited memory capacity. Although this problem is NP-complete, techniques based on the Gomory–Hu tree from network flow theory can be applied to instances of the problem to obtain a reduction in complexity. A new technique based on a graph called the inclusive cut graph is shown to be an even more powerful tool. These two techniques can solve some instances of the problem completely; still others are reduced sufficiently to be susceptible to enumerative techniques. In the worst case, the techniques yield no reduction in problem size.