The index-permutation graph model for hierarchical interconnection networks

Yeh, Chi‐Hsiang; Parhami, Behrooz

doi:10.1109/icpp.1999.797387

Cited by 5 publications

References 29 publications

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Comparing four classes of torus-based parallel architectures: Networkparameters and communication performance

Parhami

Kwai

2004

Mathematical and Computer Modelling

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The relative communication performance of low-versus high-dimensional torus networks (k-ary n-cubes) has been extensively studied under various assumptions about communication patterns and technological constraints. In this paper, we extend the comparison to torus networks with incomplete, but regular, connectivities. Taking an nD torus as the basis, we show that a simple pruning scheme can be used to reduce the node degree from 2n to 4, while preserving many of the desirable properties of the intact network. Orienting the torus links (removing half of the channels) provides a second form of pruning that leads to (multidimensional) Manhattan street networks. Finally, combined pruning and orientation yields the fourth class of toroidal networks studied here. We compare the static performance parameters of these networks and evaluate their dynamic communication performance under the assumptions of virtual cut-through switching and constant pin count. The 3D case, leading to networks that are efficiently realizable with current technology, is used to demonstrate and quantify the performance benefits. Our results reinforce, extend, and complement previous studies that have demonstrated the performance advantages of low-dimensional k-ary ncubes over higher-dimensional ones. For example pruned 3D tori provide additional design points that fall between 2D and 3D tori in terms of implementation complexity but can outperform both of these standard architectures. Thus, from a practical standpoint, pruning introduces additional flexibility in implementation options and trade-offs available to designers. (~) 2004 Elsevier Ltd. All rights reserved.

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Comparing four classes of torus-based parallel architectures: Networkparameters and communication performance

Parhami

Kwai

2004

Mathematical and Computer Modelling

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Routing and embeddings in cyclic Petersen networks: an efficient extension of the Petersen graph

Yeh

Parhami²

Proceedings of the 1999 International Conference on Parallel Processing

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The Petersen graph is a Moore graph that has node degree 3, diameter 2, and optimal network size 10. In this paper, we present a class of interconnection networks, called cyclic Petersen networks (CPNs), which efficiently extend the Petersen graph to obtain larger networks with small diameter and node degree. We derive balanced routing algorithms and efficient embeddings for CPNs. In particular, we show that many normal mesh algorithms can be emulated on CPNs with a slowdown factor of about 1.1. We also show that complete CPNs can embed meshes, tori, meshes of trees, and folded Petersen networks with dilation 3, hypercubes and generalized hypercubes with dilation 4, and pyramids with dilation 5.

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Multilayer VLSI layout for interconnection networks

Yeh

Varvarigos²,

Parhami³

Proceedings 2000 International Conference on Parallel Processing

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The index-permutation graph model for hierarchical interconnection networks

Cited by 5 publications

References 29 publications

Comparing four classes of torus-based parallel architectures: Networkparameters and communication performance

Comparing four classes of torus-based parallel architectures: Networkparameters and communication performance

Routing and embeddings in cyclic Petersen networks: an efficient extension of the Petersen graph

Multilayer VLSI layout for interconnection networks

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