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Topological properties of some interconnection network graphs
 CONGRESSUS NUMERANTIUM
, 1996
"... Interconnection networks play a vital role in parallel computing architectures. We investigate topological properties of some networks proposed for parallel computation, based on their underlying graph models. The vertices of the graph correspond to processors and the edges represent communication l ..."
Abstract

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Interconnection networks play a vital role in parallel computing architectures. We investigate topological properties of some networks proposed for parallel computation, based on their underlying graph models. The vertices of the graph correspond to processors and the edges represent communication links between processors. Parameters such as crossing number and thickness strongly affect the area required to lay out the corresponding circuit on a VLSI chip. In particular, we give upper bounds for the skewness, crossing number, and thickness of several networks including the mesh of trees, reduced mesh of trees, 2dimensional torus, butterfly, wrapped butterfly, and Benes graph.
Embedding and Emulation Results for Static Multichannel Mesh of Optical Buses
"... . We study emulation of common graphs on a ddimensional static multichannel mesh of optical buses. The target architecture consists of nodes arranged to a ddimensional nsided grid and dn d\Gamma1 optical buses. A bus is used to connect n nodes along a dimension. All nodes are connected to d bu ..."
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. We study emulation of common graphs on a ddimensional static multichannel mesh of optical buses. The target architecture consists of nodes arranged to a ddimensional nsided grid and dn d\Gamma1 optical buses. A bus is used to connect n nodes along a dimension. All nodes are connected to d buses  one per dimension. The aim in embedding graphs to such a target architecture is to minimize the number of channels used per bus, to avoid using intermediate targets in implementing the edges of the guest graph, and to minimize the physical distance between communicating nodes within each bus. We show almost optimal embedding and emulation results for butterflies and fat trees. 1 Introduction We study embedding and emulation of butterflies and fat trees. As the target architecture we consider a ddimensional nsided static multichannel mesh of optical buses [5,6], which consists of nodes arranged to a ddimensional nsided grid and dn d\Gamma1 optical buses. A bus is used to connec...