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A New Distributed Algorithm for Computing a Dominating Set on Grids

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Book cover Frontiers in Algorithmics (FAW 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9130))

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Abstract

This paper presents a new distributed algorithm that computes a dominating set of size \(\lfloor \frac{(m+2)(n+2)}{5} \rfloor -3\) on an \(m\times n\) grid, \(m,n \ge 8\). This improves upon the previous distributed algorithm of Fata et al. by 4 on the size of the found dominating set. Our result is obtained by exploring new distributed techniques for corner handling. Also, we point out an error in the termination stage of Fata et al.’s algorithm and give a corrected termination method. Our algorithm finds applications in robotics and sensor networks.

This work was partially supported by the Grant-in-Aid (MEXT/JSPS KAKENHI 15K00023).

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Notes

  1. 1.

    Note also that Chang’s constructive method has to choose from five different permutations based on input grid size.

  2. 2.

    We include vertices of super-grid in labelling for the ease of presentation.

References

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Author information

Authors and Affiliations

  1. School of Science and Technology, Tokai University, 4-1-1 Kitakaname, Hiratsuka, 259-1292, Japan

    Photchchara Pisantechakool

  2. School of Information Science and Technology, Tokai University, 4-1-1 Kitakaname, Hiratsuka, 259-1292, Japan

    Xuehou Tan

Authors
  1. Photchchara Pisantechakool
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  2. Xuehou Tan
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Corresponding author

Correspondence to Photchchara Pisantechakool .

Editor information

Editors and Affiliations

  1. Central South University, Changsha, China

    Jianxin Wang

  2. Courant Institute, New York University, New York, New York, USA

    Chee Yap

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Pisantechakool, P., Tan, X. (2015). A New Distributed Algorithm for Computing a Dominating Set on Grids. In: Wang, J., Yap, C. (eds) Frontiers in Algorithmics. FAW 2015. Lecture Notes in Computer Science(), vol 9130. Springer, Cham. https://doi.org/10.1007/978-3-319-19647-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-19647-3_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19646-6

  • Online ISBN: 978-3-319-19647-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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