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Chapter 2 Program and Network Properties ; This chapter covers fundamental properties of program behavior and introduces major classes of interconnection networks. We begin with a study of computational gran- ularity, conditions for program partitioning, matching software with hardware, program flow mechanisms, and compilation support for parallelism. Interconnection architectures introduced include static and dynamic networks. Network complexity, communication bandwidth, and data-routing capabilities are discussed. 2.1 Conditions of Parallelism The exploitation of parallelism has created a new dimension in computer science. In order to move parallel processing into the mainstream of computing, H.T. Kung (1991) has identified the need to make significant progress in three key areas: computation models for parallel computing, interprocessor communication in parallel architectures, and system integration for incorporating parallel systems into general computing envi- ronments. A theoretical treatment of parallelism is thus needed to build a basis for the above challenges. In practice, parallelism appears in various forms in a computing environ- ment. All forms can be attributed to levels of parallelism, computational granularity, time and space complexities, communication latencies, scheduling policies, and load balancing. Very often, tradeoffs exist among time, space, performance, and cost factors. 2.1.1 Data and Resource Dependences The ability to execute several program segments in parallel requires each segment to be independent of the other segments. The independence comes in various forms as defined below separately. For simplicity, to illustrate the idea, we consider the depen- dence relations among instructions in a program. In general, each code segment may contain one or more statements. We use a dependence graph to describe the relations. The nodes of a dependence graph correspond to the program statements (instructions), and the directed edges 51 
