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The Fat-Pyramid: A Robust Network For Parallel Computation, Ronald I. Greenberg
The Fat-Pyramid: A Robust Network For Parallel Computation, Ronald I. Greenberg
Ronald Greenberg
This paper shows that a fat-pyramid of area Theta(A) built from processors of size lg A requires only O(lg^2 A) slowdown in bit-times to simulate any network of area A under very general conditions. Specifically, there is no restriction on processor size (amount of attached memory) or number of processors in the competing network, nor is the assumption of unit wire delay required. This paper also derives upper bounds on the slowdown required by a fat-pyramid to simulate a network of larger area in the case of unit wire delay.
The Fat-Pyramid And Universal Parallel Computation Independent Of Wire Delay, Ronald I. Greenberg
The Fat-Pyramid And Universal Parallel Computation Independent Of Wire Delay, Ronald I. Greenberg
Ronald Greenberg
This paper shows that a fat-pyramid of area Θ(A) requires only O(log A) slowdown to simulate any competing network of area A under very general conditions. The result holds regardless of the processor size (amount of attached memory) and number of processors in the competing networks as long as the limitation on total area is met. Furthermore, the result is valid regardless of the relationship between wire length and wire delay. We especially focus on elimination of the common simplifying assumption that unit time suffices to traverse a wire regardless of its length, since the assumption becomes more and more …