This paper presents bounds on the quality of partitions induced by space-filling curves. We compare the surface that surrounds an arbitrary index range with the optimal partition in the grid, i. e. the square. It is shown that partitions induced by Lebesgue and Hilbert curves behave about 1.85 times worse with respect to the length of the surface. The Lebesgue indexing gives better results than the Hilbert indexing in worst case analysis. Furthermore, the surface of partitions based on the Lebesgue indexing are at most 5 2· √ 3 times larger than the optimal in average case.

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A performance prediction method is presented, which accurately predicts the expected program execution time on massively parallel systems. We consider distributed-memory architectures with SMD nodes and a fast communication network. The method is based on a relaxed task graph model, a queuing model, and a memory hierarchy model. The relaxed task graph is a compact representation of communicating processes of an appfication mapped onto the target machine. Simultaneous accesses to the resources of a multi-processor node are modeled by a queuing network. The execution time of the appfication is computed by an evaluation algorithm. An example application implemented on a massively parallel computer demonstrates the high accuracy of our model. Furthermore, two applications of our accurate prediction method are presented.

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