# Rectangular grid drawings of plane graphs

Session 3

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## 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## Preview

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1996