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slides
Upward Planar Morphs
Authors
A Garg
C Thomassen
+18Â more
G Battista Di
G Battista Di
G Battista Di
H Tietze
HL Smith
J Hopcroft
P Angelini
P Angelini
P Bertolazzi
P Bertolazzi
P Bertolazzi
RF Cohen
S Alamdari
S Hong
Soroush Alamdari
SS Cairns
T Biedl
T Biedl
Publication date
1 January 2018
Publisher
Doi
Cite
View
on
arXiv
Abstract
We prove that, given two topologically-equivalent upward planar straight-line drawings of an
n
n
n
-vertex directed graph
G
G
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
)
O(1)
O
(
1
)
morphing steps if
G
G
G
is a reduced planar
s
t
st
s
t
-graph,
O
(
n
)
O(n)
O
(
n
)
morphing steps if
G
G
G
is a planar
s
t
st
s
t
-graph,
O
(
n
)
O(n)
O
(
n
)
morphing steps if
G
G
G
is a reduced upward planar graph, and
O
(
n
2
)
O(n^2)
O
(
n
2
)
morphing steps if
G
G
G
is a general upward planar graph. Further, we show that
Ω
(
n
)
\Omega(n)
Ω
(
n
)
morphing steps might be necessary for an upward planar morph between two topologically-equivalent upward planar straight-line drawings of an
n
n
n
-vertex path.Comment: Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018) The current version is the extended on
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Last time updated on 10/08/2021