COCOON 1996: Computing and Combinatorics pp 92-105

# 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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