LIPIcs.GD.2024.40.pdf
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Morphing Planar Graph Drawings via Orthogonal Box Drawings
Authors
Therese Biedl 
,
Anna Lubiw ,
Jack Spalding-Jamieson
-
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Volume:
32nd International Symposium on Graph Drawing and Network Visualization (GD 2024)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Graph Drawing and Network Visualization (GD) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2024-10-28
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Therese Biedl, Anna Lubiw, and Jack Spalding-Jamieson. Morphing Planar Graph Drawings via Orthogonal Box Drawings. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.GD.2024.40
https://doi.org/10.4230/LIPIcs.GD.2024.40
Abstract
We give an algorithm to morph planar graph drawings that achieves small grid size at the expense of allowing a constant number of bends on each edge. The input is an n-vertex planar graph and two planar straight-line drawings of the graph on an O(n) × O(n) grid. The planarity-preserving morph is composed of O(n) linear morphs between successive pairs of drawings, each on an O(n) × O(n) grid with a constant number of bends per edge. The algorithm to compute the morph runs in O(n²) time on a word RAM model with standard arithmetic operations - in particular no square roots or cube roots are required.
The first step of the algorithm is to morph each input drawing to a planar orthogonal box drawing where vertices are represented by boxes and each edge is drawn as a horizontal or vertical segment. The second step is to morph between planar orthogonal box drawings. This is done by extending known techniques for morphing planar orthogonal drawings with point vertices.
Subject Classification
ACM Subject Classification
- Theory of computation → Computational geometry
Keywords
- morphing
- graph morphing
- linear morph
- planar graph drawing
- orthogonal box drawing
- orthogonal drawing
- algorithm
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References
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