Comparative Study of Product Networks

Al-Ayyoub, Abdel Elah; Day, Khaled

doi:10.1006/jpdc.2001.1770

Cited by 7 publications

(5 citation statements)

References 19 publications

(41 reference statements)

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“…[3], lead to the following conclusions for H q , where H is a PDN with n ¼ 2 þ þ 1 nodes. Corresponding results for general qD PDNs are easily formulated:1.…”

mentioning

confidence: 88%

“…þ s ¼ Oðn 1:5 Þ tracks and a total area of Oðn 3 Þ when the Oðn 0:5 Þ width of each node is taken into account. The area requirements for multidimensional PDNs follow from VLSI layout relationships for product networks [3].…”

Section: Complexity and Scalabilitymentioning

confidence: 99%

“…These two steps can be pipelined according to the scheme depicted in Fig. 4 The results presented in this section can be generalized to the case of multidimensional PDNs by means of the known properties of product networks [3]. For example, given a PDN H, optimal routing in H 2 can be accomplished via generalized "row/column" routing where a message is first routed in the "row" PDN and then in the "column" PDN, or vice versa.…”

Section: Routing and Performancementioning

confidence: 99%

“…We describe the process for H 2 , where H is a PDN, but generalization to H q or an arbitrary qD PDN is straightforward. Optimal broadcasting in H 2 follows from properties of product networks [3]: First broadcast in the row network and then in the column network, or vice versa, taking a total of four steps. All-to-all broadcasting is done by first performing all-to-all broadcasting in the row network, say, and then performing n all-to-all broadcasts in the column networks, leading to ðn þ 1Þ 2 transmission steps.…”

Section: Routing and Performancementioning

confidence: 99%

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Performance, algorithmic, and robustness attributes of perfect difference networks

Parhami

Rakov

2005

IEEE Trans. Parallel Distrib. Syst.

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Perfect difference networks (PDNs) that are based on the mathematical notion of perfect difference sets have been shown to comprise an asymptotically optimal method for connecting a number of nodes into a network with diameter 2. Justifications for, and mathematical underpinning of, PDNs appear in a companion paper. In this paper, we compare PDNs and some of their derivatives to interconnection networks with similar cost/performance, including certain generalized hypercubes and their hierarchical variants. Additionally, we discuss point-to-point and collective communication algorithms and derive a general emulation result that relates the performance of PDNs to that of complete networks as ideal benchmarks. We show that PDNs are quite robust, both with regard to node and link failures that can be tolerated and in terms of blandness (not having weak spots). In particular, we prove that the fault diameter of PDNs is no greater than 4. Finally, we study the complexity and scalability aspects of these networks, concluding that PDNs and their derivatives allow the construction of very low diameter networks close to any arbitrary desired size and that, in many respects, PDNs offer optimal performance and fault tolerance relative to their complexity or implementation cost.

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“…[3], lead to the following conclusions for H q , where H is a PDN with n ¼ 2 þ þ 1 nodes. Corresponding results for general qD PDNs are easily formulated:1.…”

mentioning

confidence: 88%

Section: Complexity and Scalabilitymentioning

confidence: 99%

Section: Routing and Performancementioning

confidence: 99%

Section: Routing and Performancementioning

confidence: 99%

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Performance, algorithmic, and robustness attributes of perfect difference networks

Parhami

Rakov

2005

IEEE Trans. Parallel Distrib. Syst.

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“…The Arrangement-Star network as a case of study on vertex product networks [1,2,3,4], it is constructed from the cross product of the Star and Arrangement graphs. It has shown to have superior topological properties over its constituents: the Star and Arrangement graphs [5,6,7].…”

Section: Introductionmentioning

confidence: 99%

Efficient Load Balancing Algorithm for the Arrangement-Star Network

Awwad¹,

Al-Sadi²

2016

ijacsa

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Abstract-The Arrangement-Star is a well-known network in the literature and it is one of the promising interconnection networks in the area of super computing, it is expected to be one of the attractive alternatives in the future for High Speed Parallel Computers. The Arrangement-Star network has many attractive topological properties such as small diameter, low degree, good connectivity, low broadcasting cost and flexibility in choosing the desired network size. Although, some of the research work has been done on Arrangement-Star network, it still needs more investigation and research efforts to explore these attractive topologies and utilize it to solve some real life applications. In this paper we attempt to fill this gap by proposing an efficient algorithm for load balancing among different processors of the Arrangement-Star network. The proposed algorithm is named as Arrangement Star Clustered Dimension Exchange Method ASCDEM presented and implemented on the Arrangement-Star network. The algorithm is based on the Clustered Dimension Exchange Method (CDEM). The ASCDEM algorithm is shown to be efficient in redistributing the load balancing among all different processors of the network as evenly as possible. A complete detail of this algorithm in addition to examples and discussions to explore the benefits of applying this distributed algorithm is presented in this paper. Furthermore an analytical study on the algorithm is presented and discussed to explore the attractive performance of the proposed algorithm.

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On anti-Kekulé and s-restricted matching preclusion problems

Lü

Zhang

2023

J Comb Optim

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Comparative Study of Product Networks

Cited by 7 publications

References 19 publications

Performance, algorithmic, and robustness attributes of perfect difference networks

Performance, algorithmic, and robustness attributes of perfect difference networks

Efficient Load Balancing Algorithm for the Arrangement-Star Network

On anti-Kekulé and s-restricted matching preclusion problems

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