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An Algorithm to Embed a Family of Node-Disjoint 3D Meshes into Locally Twisted Cubes

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Book cover Algorithms and Architectures for Parallel Processing (ICA3PP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8631))

Abstract

In this paper, embeddings of a family of 3D meshes in locally twisted cubes are studied. Let LTQ n (V, E) denotes the n-dimensional locally twisted cube. We find two major results in this paper:(1) For any integer n ≥ 4, two node-disjoint 3D meshes of size 2 ×2 ×2n − 3 can be embedded into LTQ n with dilation 1 and expansion 2. (2) For any integer n ≥ 6, four node-disjoint 4 ×2 ×2n − 5 meshes can be embedded into LTQ n with dilation 1 and expansion 4. Further, an embedding algorithm can be constructed based on our embedding method.The obtained results are optimal in the sense that the dilations of the embeddings are 1.

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Author information

Authors and Affiliations

  1. Center of Information Development and Management, Soochow University, Suzhou, 215000, China

    Yuejuan Han

Authors
  1. Lantao You
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  2. Yuejuan Han
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Illinois Institute of Technology, 60616-3793, Chicago, IL, USA

    Xian-he Sun

  2. School of Computer Science and Technology, Dalian Maritime University, 1 Linghai Road, 116026, Dalian, China

    Wenyu Qu

  3. SEECS, University of Ottawa, 8, King Edward Ave, K1N 6N5, Ottawa, ON, Canada

    Ivan Stojmenovic

  4. Deakin University, 221 Burwood Highway, 3125, Burwood, VIC, Australia

    Wanlei Zhou

  5. Dalian Maritime University, NO.1 Linhai Road Dailian, 116026, China

    Zhiyang Li

  6. BeiHang University, XueYuan Road No.37, HaiDian District, Beijing, China

    Hua Guo

  7. University of Bradford, BD7 1DP, Bradford, West Yorkshire, United Kingdom

    Geyong Min

  8. Dalian Maritime University, NO.1 Linhai Road Dailian, China, 116026

    Tingting Yang

  9. Computer Network Information Center, Chinese Academy of Sciences, 100190, Beijing, China

    Yulei Wu

  10. Shandong University, 27 Shanda Nanlu, 250100, Jinan City, Shandong Province, China

    Lei Liu

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© 2014 Springer International Publishing Switzerland

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You, L., Han, Y. (2014). An Algorithm to Embed a Family of Node-Disjoint 3D Meshes into Locally Twisted Cubes. In: Sun, Xh., et al. Algorithms and Architectures for Parallel Processing. ICA3PP 2014. Lecture Notes in Computer Science, vol 8631. Springer, Cham. https://doi.org/10.1007/978-3-319-11194-0_17

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  • DOI: https://doi.org/10.1007/978-3-319-11194-0_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11193-3

  • Online ISBN: 978-3-319-11194-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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