Tech Report CS-93-08
Space-Time Tradeoffs in Memory Hierarchies
John E. Savage
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 multilevel pebble game simulating data movement in memory hierarchies. We derive upper and lower bounds on the I/O and computation time for a number of problems, including matrix multiplication and the Fourier transform, and discuss conditions on hierarchies under which they act as fast memories.