Upward Planar Morphs

We prove that, given two topologically-equivalent upward planar straight-line drawings of an n -vertex directed graph G , there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of O (1) morphing steps i...

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Bibliographic Details
Published in:Algorithmica Vol. 82; no. 10; pp. 2985 - 3017
Main Authors: Da Lozzo, Giordano, Di Battista, Giuseppe, Frati, Fabrizio, Patrignani, Maurizio, Roselli, Vincenzo
Format: Journal Article
Language:English
Published: New York Springer US 01.10.2020
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Equivalence
Graph theory
Mathematics of Computing
Morphing
Theory of Computation
Planar morph
Graph drawing
Upward planarity
Directed graph
ISSN:0178-4617, 1432-0541
Online Access:Get full text
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Summary:We prove that, given two topologically-equivalent upward planar straight-line drawings of an n -vertex directed graph G , there always exists a morph between them such that all the intermediate drawings of the morph are upward planar and straight-line. Such a morph consists of O (1) morphing steps if G is a reduced planar st -graph, O ( n ) morphing steps if G is a planar st -graph, O ( n ) morphing steps if G is a reduced upward planar graph, and O ( n 2 ) morphing steps if G is a general upward planar graph. Further, we show that Ω ( n ) morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an n -vertex path.
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ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-020-00714-6