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

Abstract

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.

Periodically Regular Chordal Rings Are Preferable to Double-Ring Networks

“…There are preliminary indications that performance benefits do exist and could be significant in some cases. This is a direct result of the fact that our networks are quite similar to pruned torus networks that we have previously shown to be preferable to both ordinary torus networks and their unidirectional versions, known as Manhattan street networks, under most traffic conditions [29]. The node symmetry of PRC rings and their periodic regularity (the next best thing, in the absence of complete edge-symmetry) make both analytical and experimental evaluations feasible with moderate effort.…”

“…Thus, from the preceding discussions and those to follow in Sections 6 and 7, we see that such degree-3 PRC rings can advantageously replace not only double-ring networks (owing to better structural properties), but also mesh/torus networks (because of lower node degree). Furthermore, such PRC rings are comparable to pruned tori, which have been previously studied and shown to have advantages over other regular networks [29].…”

On isomorphisms and similarities between generalized Petersen networks and periodically regular chordal rings

“…5(b) shows that some PRC rings are isomorphic to ordinary pruned tori. Thus, documented advantages of pruned tori [10] carry over to PRC rings, as do comparative evaluations between pruned tori and other fixed-degree networks.…”

Bloom torus: A potential fixed interconnection architecture

“…Jellybean Machine multicomputer designed with VLSI components [9]. Tera computer academy made processor using toridial mesh [ [19,21]. Peng Zhang, Reid Powell, and Yuefan Deng constructed the interlaced bypass torus [11].…”