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Optimally Embedding 3-Ary n-Cubes into Grids

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Abstract

The 3-ary n-cube, denoted as \( {Q}_n^3 \), is an important interconnection network topology proposed for parallel computers, owing to its many desirable properties such as regular and symmetrical structure, and strong scalability, among others. In this paper, we first obtain an exact formula for the minimum wirelength to embed \( {Q}_n^3 \) into grids. We then propose a load balancing algorithm for embedding \( {Q}_n^3 \) into a square grid with minimum dilation and congestion. Finally, we derive an O(N2) algorithm for embedding \( {Q}_n^3 \) into a gird with balanced communication, where N is the number of nodes in \( {Q}_n^3 \). Simulation experiments are performed to verify the total wirelength and evaluate the network cost of our proposed embedding algorithm.

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Acknowledgment

We would like to express our sincerest appreciation to Prof. Guo-Liang Chen of University of Science and Technology of China for his constructive suggestions.

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Authors and Affiliations

  1. School of Computer Science and Technology, Soochow University, Suzhou, 215006, China

    Wei-Bei Fan, Jian-Xi Fan, Yan Wang & Yue-Juan Han

  2. Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing, 210003, China

    Wei-Bei Fan, Jian-Xi Fan & Ru-Chuan Wang

  3. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108, China

    Cheng-Kuan Lin

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  1. Wei-Bei Fan
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  4. Yan Wang
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Correspondence to Jian-Xi Fan.

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Fan, WB., Fan, JX., Lin, CK. et al. Optimally Embedding 3-Ary n-Cubes into Grids. J. Comput. Sci. Technol. 34, 372–387 (2019). https://doi.org/10.1007/s11390-019-1893-0

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  • DOI: https://doi.org/10.1007/s11390-019-1893-0

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