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The disjoint path cover in the data center network HSDC with prescribed vertices in each path

Author

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  • He, Yujia
  • Zhang, Shurong
  • Chen, Lin
  • Yang, Weihua

Abstract

The n-dimensional HSDC with the logic graph Hn is one of the most attractive server-centric data center networks for high incremental scalability. The routing design in network topology is very important for information transmission. In particular, the application of disjoint path covers can solve various problems such as program code optimization and mapping parallel programs to parallel structures. Hn consists of 2n cliques and each two vertices in a clique are adjacent. For any vertex sets {x,u} and {y,v} in W and B, respectively, and any two disjoint vertex sets A1,A2 in some clique, where (W,B) is a bipartition of Hn, in this paper, we prove that, when |Ai|≠1 and Ai∩{x,y,u,v}=∅ for i=1,2, if |A1∪A2|≤n−3, then there exists an (x,y)-path P1 and a (u,v)-path P2 in Hn passing through A1 and A2, respectively, such that P1 and P2 have no common vertices and P1∪P2 contains all vertices of Hn. Then P1∪P2 is called the 2-disjoint path cover in Hn and we propose the efficient algorithms for the path design. Furthermore, we prove that our main result is optimal.

Suggested Citation

  • He, Yujia & Zhang, Shurong & Chen, Lin & Yang, Weihua, 2023. "The disjoint path cover in the data center network HSDC with prescribed vertices in each path," Applied Mathematics and Computation, Elsevier, vol. 459(C).
    • Handle: RePEc:eee:apmaco:v:459:y:2023:i:c:s0096300323004319
    DOI: 10.1016/j.amc.2023.128262
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    References listed on IDEAS

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    1. Yang, Jinn-Shyong & Li, Xiao-Yan & Peng, Sheng-Lung & Chang, Jou-Ming, 2022. "Parallel construction of multiple independent spanning trees on highly scalable datacenter networks," Applied Mathematics and Computation, Elsevier, vol. 413(C).
    2. Qiao, Hongwei & Meng, Jixiang & Sabir, Eminjan, 2022. "Embedding spanning disjoint cycles in enhanced hypercube networks with prescribed vertices in each cycle," Applied Mathematics and Computation, Elsevier, vol. 435(C).
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