Dynamic randomized simulation of hierarchical PRAMs on meshes

The Hierarchical PRAM (H-PRAM) (T. Heywood, S. Ranka, 1992) model is a dynamically partitionable PRAM, which charges for communication and synchronization, and allows parallel algorithms to abstractly represent general locality. We show that the H-PRAM can be implemented efficiently on a two dimensional mesh. We use the Peano indexing scheme to hierarchically partition the mesh. Multiple subPRAMs of the H-PRAM are simulated on irregular submeshes. 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 specific hierarchical configuration, which may be data dependent.<
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