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Minimum-width grid drawings of plane graphs extend abstract

  • Marek Chrobak
  • Shin-ichi Nakano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 894)

Abstract

Given a plane graph G, we wish to draw it in the plane, according to the given embedding, in such a way that the vertices of G are drawn as grid points, and the edges are drawn as straight-line segments between their endpoints. An additional objective is to minimize the size of the resulting grid. It is known that each plane graph can be drawn in such a way in a (n−2)×(n−2) grid (for n≥3), and that no grid smaller than (2n/3−1)×(2n/3−1) can be used for this purpose, if n is a multiple of 3. In fact, it can be shown that, for all n≥3, each dimension of the resulting grid needs to be at least [2(n−1)/3], even if the other one is allowed to be infinite. In this paper we show that this bound is tight, by presenting a grid drawing algorithm that produces drawings of width [2(n−1)/3]. The height of the produced drawings is bounded by 4[2(n−1)/3]−1.

Keywords

Plane Graph External Face Shift Method Planar Embedding Contour Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Marek Chrobak
    • 1
  • Shin-ichi Nakano
    • 2
  1. 1.Department of Computer ScienceUniversity of CaliforniaRiverside
  2. 2.Department of System Information SciencesTohoku UniversitySendaiJapan

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