Journal of Computer Science and Technology ›› 2019, Vol. 34 ›› Issue (2): 372-387.doi: 10.1007/s11390-019-1893-0

Special Issue: Surveys; Data Management and Data Mining; Computer Networks and Distributed Computing

• Computer Networks and Distributed Computing • Previous Articles     Next Articles

Optimally Embedding 3-Ary n-Cubes into Grids

Wei-Bei Fan1,2, Member, CCF, Jian-Xi Fan1,2,*, Member, CCF, Cheng-Kuan Lin3, Member, CCF, Yan Wang1, Yue-Juan Han1, Ru-Chuan Wang2   

  1. 1 School of Computer Science and Technology, Soochow University, Suzhou 215006, China;
    2 Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing 210003, China;
    3 College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350108, China
  • Received:2018-08-08 Revised:2018-11-13 Online:2019-03-05 Published:2019-03-16
  • Contact: Jian-Xi Fan
  • About author:Wei-Bei Fan received his B.S. degree in computer science from Henan University of Urban Construction, Pingdingshan, in 2011, and received his M.S. degree in Henan University, Kaifeng, in 2014. He is currently a Ph.D. candidate in computer science at Soochow University, Suzhou. His research interests include parallel and distributed systems, algorithms, and interconnection architectures.
  • Supported by:
    This work is supported by the National Key Research and Development Program of China under Grant No. 2018YFB1003201, the National Natural Science Foundation of China under Grant Nos. 61572337, 61602261, 61672296, and 61872257, Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks Foundation under Grant No. WSNLBKF201701, the Scientific & Technological Support Project of Jiangsu Province of China under Grant Nos. BE2016777, BE2016185, and BE2017166, China Postdoctoral Science Foundation under Grant No. 172985, the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 17KJB520036, and Jiangsu Planned Projects for Postdoctoral Research Funds under Grant No. 1701172B.

The 3-ary n-cube, denoted as Qn3, 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 Qn3 into grids. We then propose a load balancing algorithm for embedding Qn3 into a square grid with minimum dilation and congestion. Finally, we derive an O(N2) algorithm for embedding Qn3 into a gird with balanced communication, where N is the number of nodes in Qn3. Simulation experiments are performed to verify the total wirelength and evaluate the network cost of our proposed embedding algorithm.

Key words: 3-ary n-cube; embedding algorithm; grid; interconnection network;

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