›› 2017, Vol. 32 ›› Issue (3): 618-629.doi: 10.1007/s11390-017-1729-8

Special Issue: Computer Architecture and Systems; Artificial Intelligence and Pattern Recognition

• Theory and Algorithms • Previous Articles     Next Articles

Optimal Path Embedding in the Exchanged Crossed Cube

Dong-Fang Zhou1, Jian-Xi Fan1,2,*, Member, CCF, Cheng-Kuan Lin1, Member, CCF, Bao-Lei Cheng1, Member, CCF, Jing-Ya Zhou1, Member, CCF, Zhao Liu1   

  1. 1. School of Computer Science and Technology, Soochow University, Suzhou 215006, China;
    2. Collaborative Innovation Center of Novel Software Technology and Industrialization, Nanjing University Nanjing 210000, China
  • Received:2016-04-21 Revised:2016-12-23 Online:2017-05-05 Published:2017-05-05
  • Contact: Jian-Xi Fan E-mail:jxfan@suda.edu.cn
  • About author:Dong-Fang Zhou received his B.S. and M.S. degrees in computer science from Huaibei Normal University, Huaibei, and University of Science and Technology of China, Hefei, in 2005 and 2012, respectively. At present, He is a Ph.D. candidate at the School of Computer Science and Technology of Soochow University, Suzhou. His research interests include computer networks, parallel and distributed systems, interconnection architectures, and cloud computing.
  • Supported by:

    This work is supported by the National Natural Science Foundation of China under Grant Nos. 61572337 and 61502328, the Program for Postgraduates Research Innovation in University of Jiangsu Province under Grant No. KYLX160126, Collaborative Innovation Center of Novel Software Technology and Industrialization, and the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant No. 14KJB520034.

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The (s + t +1)-dimensional exchanged crossed cube, denoted as ECQ(s, t), combines the strong points of the exchanged hypercube and the crossed cube. It has been proven that ECQ(s, t) has more attractive properties than other variations of the fundamental hypercube in terms of fewer edges, lower cost factor and smaller diameter. In this paper, we study the embedding of paths of distinct lengths between any two different vertices in ECQ(s, t). We prove the result in ECQ(s, t): if s > 3, t > 3, for any two different vertices, all paths whose lengths are between max{9, 「s+1/2」+「t+1/2」+4} and 2s+t+1-1 can be embedded between the two vertices with dilation 1. Note that the diameter of ECQ(s, t) is s+1/2」+「t+1/2」+2. The obtained result is optimal in the sense that the dilations of path embeddings are all 1. The result reveals the fact that ECQ(s, t) preserves the path embedding capability to a large extent, while it only has about one half edges of CQn.

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