Upper bounds on the connection probability for 2-D meshes and tori

Liang, Meilian; Xu, Xin-Shun; Liang, Jiarong; Shao, Zehui

doi:10.1016/j.jpdc.2011.11.006

Cited by 8 publications

(3 citation statements)

References 26 publications

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“…The Cartesian and strong product have a number of applications in engineering, computer science and related disciplines. They provide a setting in which to analyze many existing networks as well as to construct new and interesting networks [16,17,19,22,26]. Among various graphs products, the products which contains path and cycles have proved to be one of the most important [16,17,19].…”

Section: (Communicated By Zhipeng Cai)mentioning

confidence: 99%

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<i>L</i>(2, 1)-labeling of the Cartesian and strong product of two directed cycles

Shao¹,

Jiang²,

Vesel³

2018

Mathematical Foundations of Computing

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The frequency assignment problem (FAP) is the assignment of frequencies to television and radio transmitters subject to restrictions imposed by the distance between transmitters. One of the graph theoretical models of FAP which is well elaborated is the concept of distance constrained labeling of graphs. Let G = (V, E) be a graph. For two vertices u and v of G, we denote d(u, v) the distance between u and v. An L(2, 1)-labeling for G is a function f :The span of f is the difference between the largest and the smallest number of f (V ). The λ-number for G, denoted by λ(G), is the minimum span over all L(2, 1)-labelings of G. In this paper, we study the λ-number of the Cartesian and strong product of two directed cycles. We show that for m, n ≥ 4 the λ-number of −→ Cm2 − → Cn is between 4 and 5. We also establish the λ-number of − → C m − → C n for m ≤ 10 and prove that the λ-number of the strong product of cycles − → C m − → C n is between 6 and 8 for m, n ≥ 48.

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Section: (Communicated By Zhipeng Cai)mentioning

confidence: 99%

“…This assertion completes the proof of this case. 4,5,6,7,8,9,10,11,12,14,15,17,18,20,21,23,24,25,27,28,30,31,33,34,37,40,43,46,50,53, 56, 59}, S 7 = {3, 4,5,6,8,9,10,11,12,13,15,16,19,20,22,23,26,27,29,30,33,37,40,44, 47}, and S 10 = {3, 4,5,…”

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confidence: 99%

<i>L</i>(2, 1)-labeling of the Cartesian and strong product of two directed cycles

Shao¹,

Jiang²,

Vesel³

2018

Mathematical Foundations of Computing

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“…In 2010, Wang et al [21], [22] established lower bounds on the probability for mesh network connectivity, and gave a new fault-tolerant broadcast routing algorithm on mesh networks under the probabilistic model. Chen et al [7], and Liang et al [16] studied the connection probability for meshes, and tori, respectively. In 2007, Zhu et al [23] established the reliability of the folded hypercube.…”

Section: Index Terms-arrangement Graph Inclusion-exclusion Prinmentioning

confidence: 99%

The Reliability of Subgraphs in the Arrangement Graph

Lin

Zhou

et al. 2015

IEEE Trans. Rel.

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As the size of a multiprocessor computer system grows, the probability of having faulty (i.e., malfunctioning or failing) processors in the system increases. It is then important to quantify how the faults collectively affect the entire system. The reliability of subsystems in a system, defined as the probability that a fault-free subsystem of a certain size still exists when the system has faults, is a measure for the faults' effect on the whole system. It can be used as an indicator of system health. In this paper, we will present two schemes to calculate the reliability of an -subgraph in the -Arrangement Graph , an extensively studied interconnection network proposed for multiprocessor computers. The first scheme will use a probability fault model and the Principle of Inclusion-Exclusion to establish an upper-bound of the reliability, by taking into account the intersection of not more than three subgraphs. The second scheme uses basically the same idea, but completely neglects the intersection among subgraphs to calculate an approximate reliability. The results of the two schemes are compared, and are shown to be in good agreement, especially as the single-node reliability goes low.

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Estimating the subsystem reliability of bubblesort networks

Kung¹,

Hung²

2017

Theoretical Computer Science

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Upper bounds on the connection probability for 2-D meshes and tori

Cited by 8 publications

References 26 publications

<i>L</i>(2, 1)-labeling of the Cartesian and strong product of two directed cycles

<i>L</i>(2, 1)-labeling of the Cartesian and strong product of two directed cycles

The Reliability of Subgraphs in the Arrangement Graph

Estimating the subsystem reliability of bubblesort networks

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