Computer Science
Computer Science
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Technical Report Number TR2005-1

Title
Planar Straight-Line Grid Drawings of Binary Trees: An Experimental Study

Authors
Adrian Rusu
Department of Computer Science
Rowan University
Glassboro, NJ 08028
E-mail: rusu@rowan.edu

Radu Jianu
Department of Computer Science
Brown University
Providence, RI 02912 USA
jr@cs.brown.edu

Confesor Santiago
Department of Electrical and Computer Engineering
Rowan University
Glassboro, NJ 08028
E-mail: santia09@students.rowan.edu

Christopher Clement
Department of Computer Science
Rowan University
Glassboro, NJ 08028 USA
clemen55@students.rowan.edu

Abstract

In this paper we consider the class of binary trees and present the results of a
comprehensive experimental study on the four most representative algorithms for
drawing trees, one for each of the following tree-drawing approaches: Separation-Based
approach, Path-Based approach, Level-Based approach, Ringed Circular Layout approach.
We establish a new, simpler format for storing binary trees in files and create a
large suite of randomly-generated, unbalanced, complete, AVL, Fibonacci, and molecular
combinatory binary trees of various sizes. Our study is therefore conducted on randomly-generated,
unbalanced, and AVL binary trees with up to 50,000 nodes, on Fibonacci trees with up to 46,367
nodes, on complete binary trees with up to 65,535 = 2^16 - 1 nodes, and on molecular combinatory
binary trees with up to 50,005 nodes. Our study yields 84 charts comparing the performance of
the drawing algorithms with respect to twelve quality measures, namely Area, Aspect Ratio, Size,
Total Edge Length, Average Edge Length, Maximum Edge Length, Uniform Edge Length, Minimum Angle
Size, Average Angle Size, Angular Resolution, Closest Leaf, and Farthest Leaf. None of
the algorithms have been found to be the best in all categories.