Space-Time Tradeoffs in Memory Hierarchies
John E. Savage · 1994
The speed of CPUs is accelerating rapidly, outstripping that of peripheral storage devices and making it increasingly difficult to keep CPUs busy. Multilevel 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 simulating data movement in memory hierarchies for straight-line computations. This game provides a framework for deriving upper and lower bounds on computation time and the I/O time at each level in a memory hierarchy. We apply this framework to a representative set of problems including matrix multiplication and the Fourier transform. We also discuss conditions on hierarchies under which they act as fast flat memories.