Drawing complete binary trees inside rectilinear polygons

Abstract

Most of graph drawing algorithms draw graphs on unbounded planes. However, there are applications that require graphs to be drawn on the plane inside a given polygon. In this paper, a new algorithm for planar orthogonal drawing of complete binary trees inside rectilinear polygons is presented. Uniform distribution of nodes of graphs on drawing regions is one of the aesthetics criteria in graph drawing. The goal of this paper is to produce planar orthogonal drawings with a relatively uniform node distribution and few edge bends. The proposed algorithm can be considered as a generalization of the H-tree layout method for rectilinear polygons. A new linear time algorithm is also given for bisecting rectilinear polygons into two equi-area rectilinear sub-polygons.

Keywords:

• graph drawing
• binary tree
• rectilinear polygon
• polygon bisecting
• H-tree layout

2010 AMS Subject Classifications :

• 05C62
• 05C05
• 68W35
• 68U05
• 68U07

Acknowledgements

The Authors would like to thank anonymous referees for their useful comments and suggestions.