The fat-stack and universal routing in interconnection networks

Chen, Kevin F.; Sha, Edwin Hsing-Mean

doi:10.1016/j.jpdc.2006.01.004

“…Using the bisection method, Lemma 4.1, and an H-tree processor packing, Greenberg proved in [13] that the fat-tree can simulate any network with an O(log A) overhead under unit wire delay condition, and that the fat-pyramid can simulate any network with an O(log A) overhead regardless of wire delays, provided that the base network and the competing network are of the same area A. With similar postulates, we showed in [11] that the AFS is universal with an O(log A) overhead under both unit and nonunit wire delay conditions and is in fact the minimal network for that efficiency.…”

Section: Universality Of the Fat-stackmentioning

confidence: 57%

“…It turns out that the fat-stack is versatile as well. In a previous paper [11], we have reported the results of the fat-stack as an efficient interconnection network. The focus of this paper is to show that the universal property of the fat-stack applies to distributed networks.…”

Section: Introductionmentioning

confidence: 99%

Universal Routing and Performance Assurance for Distributed Networks

Chen

¹

,

Sha

²

2007

J. Inter. Net.

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We show that universal routing can be achieved with low overhead in distributed networks. The validity of our results rests on a new network called the fat-stack. We show that from a routing perspective the fat-stack is efficient and is suitable for use as a baseline distributed network and as a crucial benchmark architecture for evaluating the performance of specific distributed networks. We show that the fat-stack is efficient by proving it is universal. A requirement for the fat-stack to be universal is that link capacities double up the levels of the network. We use methods developed in the areas of VLSI and processor interconnect for much of our analysis. We then show how to scale the fat-stack from a VLSI graph layout to a large-scale distributed topology and how the network can be an effective benchmark architecture. Our universality proofs show that a fat-stack of area Θ(A) can simulate any competing network of area A with [Formula: see text] overhead independently of wire delay. The universality result implies that the fat-stack of a given size is nearly the best routing network of that size. The fat-stack is also the minimal universal network for an [Formula: see text] overhead in terms of number of links. Actual simulations show that the fat-stack outperforms a mesh-based distributed network of comparable hardware usage. Our work helps explain why some deployed networks function in the way they do in terms of routing. It also provides an exemplary network of proven efficiency and scalability for building new distributed systems.

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“…Bhatt and Leighton studied methods to implement fat trees and by extension fat pyramids in a VLSI layout [18] improved by DeHon for more modern multi-layer processes [19]. Fat stacks proposed by Chen and Sha are a multi-level network, where each level contains one or more subnetworks comprised of rings [20].…”

Section: Background and Related Workmentioning

confidence: 99%

Non-Uniform "Fat-Meshes" for Chip Multiprocessors

Jones

¹

2009

Parallel Process. Lett.

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This paper studies the traffic hot spots of mesh networks in the context of chip multiprocessors. To mitigate these effects, this paper describes a non-uniform fat-mesh extension to mesh networks, which are popular for chip multiprocessors. The fat-mesh is inspired by the fat-tree and dedicates additional links for connections with heavy traffic (e.g. near the center) with fewer links for lighter traffic (e.g. near the periphery). Two fat-mesh schemes are studied based on the traffic requirements of chip multiprocessors using dimensional ordered XY routing and a randomized XY-YX routing algorithms, respectively. Analytical fat-mesh models are constructed by theoretically presenting the expressions for the traffic requirements of personalized all-to-all traffic for both the raw message numbers and their normalized equivalents. We demonstrate how traffic scales for a traditional mesh compared to a non-uniform fat mesh. Simulation results demonstrate that using same number of physical links the non-uniform fat-mesh can achieve better performance than a uniform fat-mesh mesh using both synthetic traffic patterns and splash-2 benchmark traces.

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“…Bhatt and Leighton studied methods to implement fat trees and by extension fat pyramids in a VLSI layout [2] improved by DeHon for more modern multi-layer processes [6]. Fat stacks proposed by Chen and Sha are a multi-level network, where each level contains one or more subnetworks comprised of rings [4].…”

Section: Background and Related Workmentioning

confidence: 99%

Non-uniform fat-meshes for chip multiprocessors

Jones

¹

2009

2009 IEEE International Symposium on Parallel &Amp; Distributed Processing

3

0

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This paper studies the traffic hot spots of mesh networks in the context of chip multiprocessors. To mitigate these effects, this paper describes a non-uniform fat-mesh extension to mesh networks, which are popular for chip multiprocessors. The fat-mesh is inspired by the fat-tree and dedicates additional links for connections with heavy traffic (e.g. near the center) with fewer links for lighter traffic (e.g. near the periphery). Two fat-mesh schemes are studied based on the traffic requirements of chip multiprocessors using dimensional ordered XY routing and a randomized XY-YX routing algorithms, respectively. Analytical fat-mesh models are constructed by theoretically presenting the expressions for the traffic requirements of personalized all-to-all traffic for both the raw message numbers and their normalized equivalents. We demonstrate how traffic scales for a traditional mesh compared to a non-uniform fat mesh.

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The fat-stack and universal routing in interconnection networks

Cited by 4 publications

References 17 publications

Universal Routing and Performance Assurance for Distributed Networks

Universal Routing and Performance Assurance for Distributed Networks

Non-Uniform "Fat-Meshes" for Chip Multiprocessors

Non-uniform fat-meshes for chip multiprocessors

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