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Optimal st-Orientations for Plane Triangulations

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Algorithmic Aspects in Information and Management (AAIM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 4508))

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Abstract

For a plane triangulation G with n vertices, it has been proved that there exists a plane triangulation G with n vertices such that for any st-orientation of G, the length of the longest directed paths of G from s to t is \(\geq \lfloor \frac{2n}{3}\rfloor\) [18] . In this paper, we prove the bound \(\frac{2n}{3}\) is optimal by showing that every plane triangulation G with n-vertices admits an st-orientation with the length of its longest directed paths bounded by \(\frac {2n}{3}+O(1)\). In addition, this st-orientation is constructible in linear time. A by-product of this result is that every plane graph G with n vertices admits a visibility representation with height \(\le \frac{2n}{3}+O(1)\), constructible in linear time, which is also optimal.

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Authors and Affiliations

  1. Computer Science Department, University of Alabama in Huntsville, Huntsville, AL, 35899, USA

    Huaming Zhang

  2. Department of Computer Science and Engineering, SUNY at Buffalo, Buffalo, NY, 14260, USA

    Xin He

Authors
  1. Huaming Zhang
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  2. Xin He
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Ming-Yang Kao Xiang-Yang Li

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Zhang, H., He, X. (2007). Optimal st-Orientations for Plane Triangulations. In: Kao, MY., Li, XY. (eds) Algorithmic Aspects in Information and Management. AAIM 2007. Lecture Notes in Computer Science, vol 4508. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72870-2_28

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  • DOI: https://doi.org/10.1007/978-3-540-72870-2_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72868-9

  • Online ISBN: 978-3-540-72870-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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