Morphing Tree Drawings in a Small 3D Grid

Arseneva, Elena; Gangopadhyay, Rahul; Istomina, Aleksandra

doi:10.1007/978-3-030-96731-4_8

Search citation statements

Order By: Relevance

Paper Sections

Select...

Introduction1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Book1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Arseneva et al [4] proved that this is the case, as they showed that, for any two planar straightline drawings of an n-vertex tree, there exists a crossing-free (i.e., no two edges cross in any intermediate drawing) piecewise-linear 3D morph between them with O(log n) steps. Later, Istomina et al [9] gave a different algorithm for the same problem. Their algorithm uses O( √ n log n) steps, however it guarantees that any intermediate drawing of the morph lies on a 3D grid of polynomial size.…”

Section: Introductionmentioning

confidence: 99%

Morphing Planar Graph Drawings Through 3D

Buchin

Evans

Frati

et al. 2023

Lecture Notes in Computer Science

View full text Add to dashboard Cite

In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n-vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with O(n 2 ) steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.

show abstract

Section: Introductionmentioning

confidence: 99%