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- Work-preserving emulations of fixed-connection networks
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Work-preserving emulations of fixed-connection networks
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Reviews
Festus Gail Gray
Mapping a collection of processes linked by precedence and communications constraints onto the processors and routing network of a parallel machine, to take maximum advantage of the available hardware in order to minimize the completion time of the job, is one of the central problems in parallel computing. This paper addresses the problem by studying work-preserving emulations of one network type on another. An emulation is work-preserving if the slowdown is a constant factor of the ratio of the numbers of processors in the two architectures. For example, the authors show that a linear array can emulate a butterfly network in a work-preserving manner. Presumably, any algorithm that has an efficient implementation on a butterfly network can then be efficiently emulated by a linear array. This paper should interest anyone interested in efficient implementation of parallel algorithms. Full understanding requires considerable mathematical sophistication, but the general principles can be understood by anyone with a general science background. This is not the whole story, however. In the case of the linear array, the emulation of the butterfly network experienced a slowdown on the order of 2 N . The ratio of the number of processors in the butterfly to the number of processors in the linear array was exactly 2 N . From a practical viewpoint, is this an acceptable tradeoff This paper provides many theoretical results concerning the relative computational power of different types of networks of computers. If work-preserving emulations are proven not to exist, it is not possible to efficiently emulate one network by another. If work-preserving emulations do exist, it is possible to emulate one type of network on the other, but the slowdown may be unacceptable. Read the paper for details.
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