A note on optimal area algorithms for upward drawings of binary trees
Computational Geometry: Theory and Applications
Algorithms for drawing graphs: an annotated bibliography
Computational Geometry: Theory and Applications
A note on minimum-area upward drawing of complete and Fibonacci trees
Information Processing Letters
Logarithmic width, linear area upward drawing of AVL trees
Information Processing Letters
Linear area upward drawings of AVL trees
Computational Geometry: Theory and Applications - Special issue on geometric representations of graphs
Algorithms for drawing binary trees in the plane
Information Processing Letters
Area-efficient algorithms for straight-line tree drawings
Computational Geometry: Theory and Applications
Optimizing Area and Aspect Ratio in Straight-Line Orthogonal Tree Drawings
GD '96 Proceedings of the Symposium on Graph Drawing
An experimental study on algorithms for drawing binary trees
APVis '06 Proceedings of the 2006 Asia-Pacific Symposium on Information Visualisation - Volume 60
Tree Drawings on the Hexagonal Grid
Graph Drawing
Journal of Discrete Algorithms
Area-efficient order-preserving planar straight-line drawings of ordered trees
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
Three-dimensional drawings of bounded degree trees
GD'06 Proceedings of the 14th international conference on Graph drawing
Straight-line drawings of general trees with linear area and arbitrary aspect ratio
ICCSA'03 Proceedings of the 2003 international conference on Computational science and its applications: PartIII
Straight-line orthogonal drawings of binary and ternary trees
GD'07 Proceedings of the 15th international conference on Graph drawing
Drawing ordered (k - 1)-ary trees on k-grids
GD'10 Proceedings of the 18th international conference on Graph drawing
Drawing trees with perfect angular resolution and polynomial area
GD'10 Proceedings of the 18th international conference on Graph drawing
Drawing unordered trees on k-grids
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Hi-index | 0.00 |
We investigate the problem of drawing an arbitrary n-node binary tree orthogonally and upwardly in an integer grid using straight-line edges. We show that one can simultaneously achieve good area bounds while also allowing the aspect ratio to be chosen as a fixed constant or a parameter under the user's control. In addition, we show that one can also achieve an additional desirable aesthetic criterion, which we call "subtree separation". Our drawings require O(n logn) area, which we show is optimal to within constant factors in the worst case (i.e. there are trees that need Ω(n logn) area for any upward orthogonal straight-line drawing with good aspect ratio). An improvement for non-upward drawings is briefly mentioned.