Hamiltonicity of the basic WK-recursive pyramid with and without faulty nodes

Wang, Yichun; Juan, Justie Su-Tzu

doi:10.1016/j.tcs.2014.10.034

Cited by 10 publications

(3 citation statements)

References 14 publications

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“…For example, adding an "open edge" to each of the k extreme vertices in Sierpiński graphs yields the WK-recursive networks. These resultant networks have many favorable structure properties, including a high degree of regularity, symmetry and scalability, which can be applied as a model of interconnection networks widely used in implementing large-scale distributed systems [67], [68]. Recently, great efforts have been dedicated to investigating various issues of the WK-Recursive networks, such as topological properties [69], broadcasting algorithms [70], and fault tolerance [71].…”

Section: B Sierpiński Graphsmentioning

confidence: 99%

Consensus in Self-Similar Hierarchical Graphs and Sierpiński Graphs: Convergence Speed, Delay Robustness, and Coherence

Zhang

et al. 2019

IEEE Trans. Cybern.

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The hierarchical graphs and Sierpiński graphs are constructed iteratively, which have the same number of vertices and edges at any iteration, but exhibit quite different structural properties: the hierarchical graphs are nonfractal and small-world, while the Sierpiński graphs are fractal and ''large-world.'' Both graphs have found broad applications. In this paper, we study consensus problems in hierarchical graphs and Sierpiński graphs, focusing on three important quantities of consensus problems, that is, convergence speed, delay robustness, and coherence for first-order (and second-order) dynamics, which are, respectively, determined by algebraic connectivity, maximum eigenvalue, and sum of reciprocal (and square of reciprocal) of each nonzero eigenvalue of Laplacian matrix. For both graphs, based on the explicit recursive relation of eigenvalues at two successive iterations, we evaluate the second smallest eigenvalue, as well as the largest eigenvalue, and obtain the closed-form solutions to the sum of reciprocals (and square of reciprocals) of all nonzero eigenvalues. We also compare our obtained results for consensus problems on both graphs and show that they differ in all quantities concerned, which is due to the marked difference of their topological structures.

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Section: B Sierpiński Graphsmentioning

confidence: 99%

Consensus in Self-Similar Hierarchical Graphs and Sierpiński Graphs: Convergence Speed, Delay Robustness, and Coherence

Zhang

et al. 2019

IEEE Trans. Cybern.

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“…So the network-on-chip (NoC) topology design is an important factor in the on-chip multicore architecture. Our team proposed the triplet-based multicore architecture (TriBA) on-chip network is a kind of the multicore WK-recursive network [3,4], which has several advantages such as scalability, regularity, locality and hierarchy.…”

Section: Introductionmentioning

confidence: 99%

KLSAT: An Application Mapping Algorithm Based on Kernighan–Lin Partition and Simulated Annealing for a Specific WK-Recursive NoC Architecture

Wang

Shi

Zhang

2019

Lecture Notes in Computer Science

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Application mapping is a critical phase in NoC design because of the running time, the network latency and the power consumption. In order to reduce these problems of applications running on multicore architecture, we propose a novel application mapping algorithm, called KLSAT mapping algorithm. It is used for the triplet-based architecture (TriBA) topology which is WK-recursive based networks well conform to a modular design due to the properties of regularity and scalability. The KLSAT mapping algorithm exploits the advantage of both the KernighanLin partitioning algorithm and simulated annealing algorithm to reduce the overall power consumption and network latency. Compared to the random mapping algorithm, the experiment results reveal that the solutions generated by the proposed mapping algorithm reduce average power consumption and network latency by 6.4%, 12.2% in mapping 27 cores and 29.5%, 26.7% in mapping 81 cores respectively.

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“…Introduction: The network-on-chip (NoC) topology plays a crucial role in the current multi-core processor. The triplet-based WK-recursive (TriBA) network is a subclass of the WK-recursive [1,2] network, which has several advantages such as hierarchy, scalability, regularity, robust topology and symmetry. Among these properties, the hierarchy and regularity are the most valuable properties in which all the on-chip fabrics (cache banks, cores and routers) are hierarchically connected by grouping basic modules through a NoC.…”

mentioning

confidence: 99%

Hybrid WK‐recursive on‐chip network for multi‐core system

Shi

Cai

2017

Electron. lett.

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WK-recursive based networks well conform to a modular design due to the properties of regularity and scalability. Here, the focus is on a triplet-based WK-recursive topology and its implementation using tiled shapes in multi-core processors design is explored. To further improve the network throughput and reduce the network latency, a pair of heterogeneous topologies is proposed to separate the core communication from the memory communication. It is demonstrated that the triangular topologies are feasible to be implemented with rectangular tile floor-planning.

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Hamiltonicity of the basic WK-recursive pyramid with and without faulty nodes

Cited by 10 publications

References 14 publications

Consensus in Self-Similar Hierarchical Graphs and Sierpiński Graphs: Convergence Speed, Delay Robustness, and Coherence

Consensus in Self-Similar Hierarchical Graphs and Sierpiński Graphs: Convergence Speed, Delay Robustness, and Coherence

KLSAT: An Application Mapping Algorithm Based on Kernighan–Lin Partition and Simulated Annealing for a Specific WK-Recursive NoC Architecture

Hybrid WK‐recursive on‐chip network for multi‐core system

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