Translating submachine locality into locality of reference

In this work, we show that the submachine locality exposed by hierarchical bulk-synchronous computations can be efficiently turned into locality of reference on arbitrarily deep hierarchies. Specifically, we develop efficient schemes to simulate parallel programs written for the Decomposable BSP (a BSP variant which features a hierarchical decomposition into submachines) on the sequential Hierarchical Memory Model (HMM), which rewards the exploitation of temporal locality, and on its extension with block transfer, the BT model, which also rewards the exploitation of spatial locality. The simulations yield good hierarchy-conscious sequential algorithms from parallel ones, and provide evidence of the strict relation between submachine locality in parallel computation and locality of reference in the hierarchical memory setting. We also devise a generalization of the HMM result to the self-simulation of D-BSP augmented with hierarchical memory modules, which yields an interesting analog of Brent's lemma, thus proving that the enhanced model features a seamless integration of memory and network hierarchies.