Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.
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Transcript of Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.
![Page 1: Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.](https://reader038.fdocuments.in/reader038/viewer/2022110405/56649efb5503460f94c0d895/html5/thumbnails/1.jpg)
Topological Morphing of Planar Graphs
Bertinoro Workshop on Graph Drawing 2012
![Page 2: Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.](https://reader038.fdocuments.in/reader038/viewer/2022110405/56649efb5503460f94c0d895/html5/thumbnails/2.jpg)
Topological Morphing
Given two planar embeddings of the same graph, how many operations do we need to morph an
embedding into the other one?
A planar embedding is composed of a combinatorial embedding (rotation scheme) + an external face
We defined the problem as “Topological Morphing” in analogy with the “Geometric Morphing”, in which a planar drawing is morphed into another.
![Page 3: Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.](https://reader038.fdocuments.in/reader038/viewer/2022110405/56649efb5503460f94c0d895/html5/thumbnails/3.jpg)
Geometric Morphing
Geometric morphing modifies the shape of the objects in the drawing, while maintaining the topology unchanged
![Page 4: Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.](https://reader038.fdocuments.in/reader038/viewer/2022110405/56649efb5503460f94c0d895/html5/thumbnails/4.jpg)
Topological morphing modifies the arrangement of the objects in the drawing
Topological vs Geometric Morphing
![Page 5: Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.](https://reader038.fdocuments.in/reader038/viewer/2022110405/56649efb5503460f94c0d895/html5/thumbnails/5.jpg)
State of the Art
Angelini, Cortese, Di Battista, Patrignani. Topological Morphing of Planar Graphs, GD’08
Definition of two operations to modify the embedding of a biconnected graphFlip & Skip
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Operations - Flip
A flip operation “flips” a subgraph with respect to a split pair
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Operations - Flip
A flip operation is not allowed if the subgraph to be flipped contains all the edges of the external face
![Page 8: Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.](https://reader038.fdocuments.in/reader038/viewer/2022110405/56649efb5503460f94c0d895/html5/thumbnails/8.jpg)
Operations - Skip
A skip operation moves the external face to an adjacent face with respect to a separation pair
![Page 9: Topological Morphing of Planar Graphs Bertinoro Workshop on Graph Drawing 2012.](https://reader038.fdocuments.in/reader038/viewer/2022110405/56649efb5503460f94c0d895/html5/thumbnails/9.jpg)
Operations - Skip
A skip operation does not change any rotation scheme
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State of the Art
The problem of minimizing the number of such operations is NP-Complete (Sorting by Reversals)
Polynomial-time algorithms if the combinatorial embedding is fixed if there is no parallel component
FPT-algorithm
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Open Problem
Simply-connected planar graphs Definition of allowed operations
Each configuration has to be reachable The mental map of the user must be preserved
Study of the problem of minimizing the number of such operations
Biconnected planar graphs Give a weight to each operation depending on the size
of the involved component
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