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.

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Copyright information

© Springer-Verlag 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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