Work-preserving real-time emulation of meshes on butterfly networks

The emulation of a guest network G on a host network H is work-preserving and real-time if the inefficiency, that is the ratio WG/WH of the amounts of work done in both networks, and the slowdown of the emulation are O(1). In this thesis we show that an infinite number of meshes can be emulated on a butterfly in a work-preserving real-time manner, despite the fact that any emulation of an s x s-node mesh in a butterfly with load 1 has a dilation of Ω(logs). The recursive embedding of a mesh in a butterfly presented by Koch et al. (STOC 1989), which forms the basis for our work, is corrected and generalized by relaxing unnecessary constraints. An algorithm determining the parameter for each stage of the recursion is described and a rigorous analysis of the resulting emulation shows that it is work-preserving and real-time for an infinite number of meshes. Data obtained from simulated embeddings suggests possible improvements to achieve a truly work-preserving emulation of the class of meshes on the class of butterflies

On relations between arrays of processing elements of different dimensionality

We are examining the power of $d$-dimensional arrays of processing elements in view of a special kind of structural complexity. In particular simulation techniques are shown, which allow to reduce the dimension at an increased cost of time only. Conversely, it is not possible to regain the speed by increasing the dimension. Moreover, we demonstrate that increasing the computation time (just by a constant factor) can have a more favorable effect than increasing the dimension (arbitrari

Optimal Emulation of Meshes on Meshes of Trees

. Many problems can be solved more efficiently on a mesh of trees network than on a mesh. Until now it has been an open problem whether the mesh of trees is always at least as fast as the mesh. In this paper, we present an emulation of N-node meshes on O(N)-node meshes of trees with constant slowdown, even though any embedding of a mesh into a mesh of trees requires dilation\Omega (log N ). This demonstrates that the mesh of trees is strictly more powerful than the mesh. As an application, we show how to construct an optimal O( p N) sorting algorithm for the mesh of trees that improves on the best previously known algorithm by a logarithmic factor. 1 Introduction Fixed interconnection networks for parallel computers determine to a large degree the algorithms used. They define the available locality any algorithm must try to exploit to be efficient. One of the important questions regarding interconnection networks is their relative computational power which can be determined by emula..

On Relations Between Arrays of Processing Elements of Different Dimensionality

We are examining the power of d-dimensional arrays of processing elements in view of a special kind of structural complexity. In particular simulation techniques are shown, which allow to reduce the dimension at an increased cost of time only. Conversely, it is not possible to regain the speed by increasing the dimension. Moreover, we demonstrate that increasing the computation time (just by a constant factor) can have a more favorable effect than increasing the dimension (arbitrarily). 1 Introduction We can regard d-dimensional arrays of processing elements as models for massively parallel computers. A usual step towards a formal model is to treat the single processing elements as finite-state machines. Various types of such devices have been studied under manifold aspects for a long time (see e.g. [2, 4, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 18, 19]). Mainly, the types differ in how the single machines are interconnected and in how the input is supplied. Here we are investigating d-di..