Extending the Hong-Kung model to memory hierarchies
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The speed of CPUs is accelerating rapidly, outstripping that of peripheral storage devices and making it increasingly difficult to keep CPUs busy. Consequently multi-level memory hierarchies, scaled to simulate single-level memories, are increasing in importance. In this paper we introduce the Memory Hierarchy Game, a multi-level pebble game that simulates data movement in memory hierarchies in terms of which we study space-time tradeoffs.
We provide a) a common generalization of the Hong-Kung and Paterson-Hewitt pebble models to the Memory Hierarchy Game, b) a greatly simplified proof of the Hong-Kung lower bound on I/O complexity that makes their result readily accessible, c) straight-line algorithms for a representative set of problems that are simultaneously optimal at each level in the memory hierarchy in their use of space and I/O and computation time, and d) an extension the game to block transfers of data between memories.
KeywordsFast Fourier Transform Discrete Fourier Transform Computation Step Memory Hierarchy Matrix Multiplication Algorithm
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