Journal of Computer Science and Technology

, Volume 34, Issue 2, pp 372–387 | Cite as

Optimally Embedding 3-Ary n-Cubes into Grids

  • Wei-Bei Fan
  • Jian-Xi FanEmail author
  • Cheng-Kuan Lin
  • Yan Wang
  • Yue-Juan Han
  • Ru-Chuan Wang
Regular Paper


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.


3-ary n-cube embedding algorithm grid interconnection network 


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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.

Supplementary material

11390_2019_1893_MOESM1_ESM.pdf (299 kb)
ESM 1 (PDF 299 kb)


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Copyright information

© Springer Science+Business Media, LLC & Science Press, China 2019

Authors and Affiliations

  • Wei-Bei Fan
    • 1
    • 2
  • Jian-Xi Fan
    • 1
    • 2
    Email author
  • Cheng-Kuan Lin
    • 3
  • Yan Wang
    • 1
  • Yue-Juan Han
    • 1
  • Ru-Chuan Wang
    • 2
  1. 1.School of Computer Science and TechnologySoochow UniversitySuzhouChina
  2. 2.Jiangsu High Technology Research Key Laboratory for Wireless Sensor NetworksNanjingChina
  3. 3.College of Mathematics and Computer ScienceFuzhou UniversityFuzhouChina

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