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This paper outlines a cost-effective multiprocessor architecture that takes into consideration the importance of hardware and software costs as well as delivered performance in the context of real applications. The proposed architecture, HPAM, is organized as a hierarchy of processors-and-memory subsystems. Each subsystem contains a homogeneous parallel machine. Across the levels of the hierarchy, processor speeds and interconnection technology vary. The HPAM design is driven by several considerations: the observed characteristics of real applications, cost-efficiency considerations and the need for ease-of-usage. Rationales and the results of a preliminary study that motivated the design of this architecture are presented. These results include benchmark data that expose the advantages of HPAM over other architectures. Technology trends that support the desirability and viability of the proposed machine organization are also presented. Two classes of applications that demand 100 Teraops computation rates and that will drive future HPAM work are discussed. Furthermore a flexible software environment is proposed for this architecture, which facilitates several programming scenarios: automatic program translation, library based programming and performance-guided coding by expert programmers.