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Rectangular grid drawings of plane graphs

  • Saidur Rahman
  • Shin-ichi Nakano
  • Takao Nishizeki
Session 3
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1090)

Abstract

The rectangular grid drawing of a plane graph G is a drawing of G such that each vertex is located on a grid point, each edge is drawn as a horizontal or vertical line segment, and the contour of each face is drawn as a rectangle. In this paper we give a simple linear-time algorithm to find a rectangular grid drawing of G if it exists. We also give an upper bound \(W + H \leqslant \frac{n}{2}\)on the sum of required width W and height H and a bound \(W + H \leqslant \frac{{n^2 }}{{16}}\)on the area of a rectangular grid drawing of G, where n is the number of vertices in G. These bounds are best possible, and hold for any compact rectangular grid drawing.

Keywords

Algorithm Rectangular drawing Grid drawing Grid area Floorplanning 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Saidur Rahman
    • 1
  • Shin-ichi Nakano
    • 1
  • Takao Nishizeki
    • 1
  1. 1.Graduate School of Information SciencesTohoku UniversitySendaiJapan

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