Upper bounds to processor-time tradeoffs under bounded-speed message propagation

Upper bounds are derived for the processor-time tradeoffs of machines such as linear arrays and two-dimensional meshes, which are compatible with the physical limitation expressed by bounded-speed propagation of messages (due to the finiteness of the speed of light). It is shown that parallelism and locality combined may yield speedups superlinear in the number of processors. The speedups are inherent, due to the optimality of the obtained tradeoffs as established in a companion paper. Simulations are developed of multiprocessor machines by analogous machines with fewer processors. A crucial role is played by the hierarchical nature of the memory system. A divide-and-conquer technique for hierarchical memories is developed, based on the graph-theoretic notion of topological separator. For multiprocessors, this technique also requires a careful balance of memory access and interprocessor communication costs, which leads to non-intuitive orchestrations of the simulation process.