Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

UPRIGHT DRAWINGS OF GRAPHS ON THREE LAYERS

  • Alam, Muhammad Jawaherul (Graph Drawing Research Group, Department of CSE, Bangladesh University of Engineering and Technology (BUET)) ;
  • Rabbi, Md. Mashfiqui (Department of CS, Dartmouth college) ;
  • Rahman, Md. Saidur (Graph Drawing Research Group, Department of CSE, Bangladesh University of Engineering and Technology (BUET)) ;
  • Karim, Md. Rezaul (Department of CSE, University of Dhaka)
  • 투고 : 2010.01.29
  • 심사 : 2010.03.04
  • 발행 : 2010.09.30
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초록

An upright drawing of a planar graph G on k layers is a planar straight-line drawing of G, where the vertices of G are placed on a set of k horizontal lines, called layers and no two adjacent vertices are placed on the same layer. There is a previously known algorithm that decides in linear time whether a planar graph admits an upright drawing on k layers for a fixed value of k. However, the constant factor in the running time of the algorithm increases exponentially with k and makes it impractical even for k = 3. In this paper, we give a linear-time algorithm to examine whether a biconnected planar graph G admits an upright drawing on three layers and to obtain such a drawing if it exists. We also give a necessary and sufficient condition for a tree to have an upright drawing on three layers. Our algorithms in both the cases are much simpler and easier to implement than the previously known algorithms.

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참고문헌

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