A general framework for developing adaptive fault-tolerant routing algorithms

El‐Ghazawi, Tarek; Youssef, Abdou

doi:10.1109/24.229494

Cited by 15 publications

(9 citation statements)

References 13 publications

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“…General studies about various properties of Cartesian product networks have also been reported [7], [8], [9], [10]. In particular, [9] studies fault tolerance properties of product networks, including results on node-connectivity and adaptive fault-tolerant routing. In this paper, we contribute to the study of this class of networks by investigating their fault tolerance properties.…”

Section: Introductionmentioning

confidence: 98%

“…Examples of studied product networks include products of Petersen graphs [1], [2], mesh-connected trees [3], product-shuffle [4], hyper-deBruijn [5], and banyan-hypercube networks [6]. General studies about various properties of Cartesian product networks have also been reported [7], [8], [9], [10]. In particular, [9] studies fault tolerance properties of product networks, including results on node-connectivity and adaptive fault-tolerant routing.…”

Section: Introductionmentioning

confidence: 98%

“…D URING the last decade, a substantial amount of research [1], [2], [3], [4], [5], [6], [7], [8], [9], [10] has investigated the viability of Cartesian product graphs as interconnection networks for multiprocessor systems. A Cartesian product graph (or network) is obtained by applying the graph Cartesian product operation on factor networks.…”

Section: Introductionmentioning

confidence: 99%

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Minimal fault diameter for highly resilient product networks

Day

Al-Ayyoub

2000

IEEE Trans. Parallel Distrib. Syst.

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AbstractÐWe present a number of results related to the fault tolerance of Cartesian product networks. We start by presenting a method for building containers (i.e., sets of node-disjoint paths) between any two nodes of a product network based on given containers for the factor networks. Then, we show that the best achievable fault diameter (i.e., diameter under maximum fault conditions), under reasonable network regularity and connectivity conditions, is equal to the fault-free diameter plus one. The concept of high fault resilience is then defined. We then prove that if each factor network is highly resilient, then their Cartesian product has minimal fault diameter. We derive from these results that Cartesian products of several popular networks are highly resilient and have minimal fault diameter equal to diameter plus one. These results spare future efforts that would be needed to individually determine the fault diameter of such networks as has been the practice with previously studied networks.

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Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Minimal fault diameter for highly resilient product networks

Day

Al-Ayyoub

2000

IEEE Trans. Parallel Distrib. Syst.

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“…Examples of product networks that have been investigated include hyper-Petersen [32], folded Petersen cube [43], mesh connected trees [33], product shuffle [35], and hyper-deBruijn [34]. El-Ghazawi and Youssef studied in [40] the connectivity and fault tolerance of product networks. They also showed how to achieve adaptive fault-tolerant routing algorithms based on ones written for the component networks.…”

Section: Introductionmentioning

confidence: 98%

The Hyperstar Interconnection Network

Al-Ayyoub

Day

1998

Journal of Parallel and Distributed Computing

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“…Many other product networks have been proposed recently, such as products of de Bruijn networks [9], [29], products of Petersen graphs [26], and mesh-connected trees [8], [9] (which are products of complete binary trees). As a general class, routing properties of product networks have been studied in [4], [12]. Topological and embedding properties of product networks have been analyzed in [9], and VLSI complexity of product networks has been analyzed in [10].…”

Section: Introductionmentioning

confidence: 99%

Generalized algorithm for parallel sorting on product networks

Fernández¹,

Efe

1997

IEEE Trans. Parallel Distrib. Syst.

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We generalize the well-known odd-even merge sorting algorithm, originally due to Batcher [2], and show how this generalized algorithm can be applied to sorting on product networks. If G is an arbitrary factor graph with N nodes, its r-dimensional product contains N r nodes. Our algorithm sorts N r keys stored in the r-dimensional product of G in O r F N (2 time, where F(N) depends on G. We show that, for any factor graph G, F(N) is, at most, O(N), establishing an upper bound of O r N ( ) 2 for the time complexity of sorting N r keys on any product network. For product networks with bounded r (e.g., for grids), this leads to the asymptotic complexity of O(N) to sort N r keys, which is optimal for several instances of product networks. There are factor graphs for which F N O N ( ) (log ) 2 , which leads to the asymptotic running time of O N (log ) 2 to sort N r keys. For networks with bounded N (e.g., in the hypercube N = 2, fixed), the asymptotic complexity becomes O r ( ) 2 .We show how to apply the algorithm to several cases of well-known product networks, as well as others introduced recently. We compare the performance of our algorithm to well-known algorithms developed specifically for these networks, as well as others. The result of these comparisons led us to conjecture that the proposed algorithm is probably the best deterministic algorithm that can be found in terms of the low asymptotic complexity with a small constant.

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A general framework for developing adaptive fault-tolerant routing algorithms

Cited by 15 publications

References 13 publications

Minimal fault diameter for highly resilient product networks

Minimal fault diameter for highly resilient product networks

The Hyperstar Interconnection Network

Generalized algorithm for parallel sorting on product networks

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