Dynamic Randomized Simulation of Hierarchical PRAMs on Meshes

The Hierarchical PRAM (H-PRAM) 5] model is a dynamically partitionable PRAM, which charges for communication and synchronization, and allows parallel algorithms to abstractly represent general locality. In this paper we show that the H-PRAM can be implemented eeciently on a two-dimensional mesh. We use the Peano indexing scheme to hierarchically partition the mesh. Multiple sub-PRAMs of the H-PRAM are simulated on irregular sub-meshes. For an H-PRAM program of cost T, the overall CRCW H-PRAM simulation runs in time constant in T with high probability. The simulation is dynamic, i.e. it does not depend on prior knowledge of a program's speciic hierarchical connguration, which may be data dependent.