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Simultaneous Drawing of Planar Graphs with Right-Angle Crossings and Few Bends

2016
*
Journal of Graph Algorithms and Applications
*

*graphs*form

*right*

*angles*. ... Given two

*planar*

*graphs*that are defined on the same set

*of*vertices, a RAC

*simultaneous*

*drawing*is one in which each

*graph*is drawn

*planar*, there are no edge overlaps

*and*the

*crossings*between the two ... JGAA'13]A

*Few*Known ResultsAny pair

*of*trees admits an SE

*drawing*

*with*1

*bend*

*and*quadratic area.Any pair

*of*

*planar*

*graphs*admits an SE

*drawing*

*with*2

*bends*

*and*quadratic area. small

*angles*A cycle

*and*...

##
###
Simultaneous Drawing of Planar Graphs with Right-Angle Crossings and Few Bends
[chapter]

2015
*
Lecture Notes in Computer Science
*

JGAA'13]A

doi:10.1007/978-3-319-15612-5_20
fatcat:ijimgembw5fj7eijhry2nboks4
*Few*Known ResultsAny pair*of*trees admits an SE*drawing**with*1*bend**and*quadratic area.Any pair*of**planar**graphs*admits an SE*drawing**with*2*bends**and*quadratic area. small*angles*A cycle*and*... Any pair*of*trees admits an SE*drawing**with*1*bend**and*quadratic area.Any pair*of**planar**graphs*admits an SE*drawing**with*2*bends**and*quadratic area.small*angles*A cycle*and*a matching always admit a geometric ... Wheel × Matching All*graphs*are drawn on the O(n) × O(n)-grid. All algorithms run in O(n) time. Sefe Rac- ...##
###
Simultaneous Embeddings with Few Bends and Crossings

2019
*
Journal of Graph Algorithms and Applications
*

A

doi:10.7155/jgaa.00507
fatcat:mazzfptm75havkdnlfwrmqwmue
*simultaneous*embedding*with*fixed edges (Sefe)*of*two*planar**graphs*R*and*B is a pair*of*plane*drawings**of*R*and*B that coincide when restricted to their common vertices*and*edges. ... We show that whenever R*and*B admit a Sefe, they also admit a Sefe in which every edge is a polygonal curve*with**few**bends**and*every pair*of*edges has*few**crossings*. ... This research initiated at the Workshop on Geometry*and**Graphs*, held at the Bellairs Research Institute in Barbados in March 2015. ...##
###
Simultaneous Embeddings with Few Bends and Crossings
[article]

2015
*
arXiv
*
pre-print

A

arXiv:1508.07921v1
fatcat:tramroskzzd35dbsaycm57oeae
*simultaneous*embedding*with*fixed edges (SEFE)*of*two*planar**graphs*R*and*B is a pair*of*plane*drawings**of*R*and*B that coincide when restricted to the common vertices*and*edges*of*R*and*B. ... We show that whenever R*and*B admit a SEFE, they also admit a SEFE in which every edge is a polygonal curve*with**few**bends**and*every pair*of*edges has*few**crossings*. ... Acknowledgments This research initiated at the Workshop on Geometry*and**Graphs*, held at the Bellairs Research Institute in Barbados in March 2015. ...##
###
A Survey on Graph Drawing Beyond Planarity
[article]

2018
*
arXiv
*
pre-print

*Graph*

*Drawing*Beyond

*Planarity*is a rapidly growing research area that classifies

*and*studies geometric representations

*of*non-

*planar*

*graphs*in terms

*of*forbidden

*crossing*configurations. ... Aim

*of*this survey is to describe the main research directions in this area, the most prominent known results,

*and*some

*of*the most challenging open problems. ... (c) A straight-line

*drawing*computed

*with*a force-directed algorithm (left)

*and*a subsequent

*drawing*

*with*improved

*crossing*

*angle*resolution, obtained using smoothed curves (

*right*). ...

##
###
Simultaneous graph embedding with bends and circular arcs

2009
*
Computational geometry
*

We demonstrate how to

doi:10.1016/j.comgeo.2008.05.003
fatcat:6utifpbxjrbyfhqzqa2tpiudam
*simultaneously*embed a path*and*an n-level*planar**graph**and*how to use radial embeddings for curvilinear*simultaneous*embeddings*of*a path*and*an outerplanar*graph*. ... We also show how to use star-shaped levels to find 2-*bends*per path edge*simultaneous*embeddings*of*a path*and*an outerplanar*graph*. All embedding algorithms run in O (n) time. ...*With*level*and*radial embeddings*of**graphs*, we improve on this result to obtain a*planar**simultaneous*embedding*of*an n-vertex*planar**graph*G*with*no edge*bends**and*an n-vertex path P , which may have ...##
###
Planar Polyline Drawings with Good Angular Resolution
[chapter]

1998
*
Lecture Notes in Computer Science
*

To our best knowledge, this algorithm achieves the best

doi:10.1007/3-540-37623-2_13
fatcat:vwhqc4rlmrenrpmo4gsdziohqm
*simultaneous*bounds concerning the grid size, angular resolution,*and*number*of**bends*for*planar*grid*drawings**of*high-degree*planar**graphs*. ... We present a linear time algorithm that constructs a*planar*polyline grid*drawing**of*any plane*graph**with*n vertices*and*maximum degree d on a (2n − 5) × ( 3 2 n − 7 2 ) grid*with*at most 5n − 15*bends*... Important aesthetic criteria for nice*drawings*are: a small number*of*edge*crossings*, small area,*few**bends*,*and*a good angular resolution (see, e.g., [27] ). ...##
###
Semi-bipartite Graph Visualization for Gene Ontology Networks
[chapter]

2010
*
Lecture Notes in Computer Science
*

*Angle*

*Crossing*(RAC)

*drawings*are poly-line

*drawings*where each

*crossing*forms four

*right*

*angles*. ... ,

*and*study tradeoffs between the

*crossing*resolution (i.e., the minimum

*angle*formed by two

*crossing*segments), the curve complexity (i.e., maximum number

*of*

*bends*per edge), the total number

*of*

*bends*...

##
###
Non-planar Orthogonal Drawings with Fixed Topology
[chapter]

2005
*
Lecture Notes in Computer Science
*

We present a procedure for calculating the

doi:10.1007/978-3-540-30577-4_13
fatcat:d732fxv47bgothe6eplysc7deq
*bend*minimal shape*of*non-*planar**graphs**with*given topology. ... In this paper we extend the*drawing*standard to the class*of*non-*planar**graphs**and*present an algorithm that computes provably*bend*-minimal*drawings*within this standard. ... They have between 10*and*100 nodes each,*and*most*of*them are non-*planar*. But even the non-*planar**graphs*are quite sparse*and*have therefore very*few*dummy-nodes after the*planarization*step. ...##
###
Drawing Partially Embedded and Simultaneously Planar Graphs

2015
*
Journal of Graph Algorithms and Applications
*

We investigate the problem

doi:10.7155/jgaa.00375
fatcat:i7opm6avcngzrcx73dfekq4jpm
*of*constructing*planar**drawings**with**few**bends*for two related problems, the partially embedded*graph*problem-to extend a straight-line*planar**drawing**of*a subgraph to a*planar*...*drawing**of*the whole*graph*-*and*the*simultaneous**planarity*problem-to find*planar**drawings**of*two*graphs*that coincide on shared vertices*and*edges. ... The authors would like to thank the anonymous referees for their useful comments*and*suggestions. ...##
###
Drawing Partially Embedded and Simultaneously Planar Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

We investigate the problem

doi:10.1007/978-3-662-45803-7_3
fatcat:7kjeaklwazhy7ph3qlrh4k6a4m
*of*constructing*planar**drawings**with**few**bends*for two related problems, the partially embedded*graph*problem-to extend a straight-line*planar**drawing**of*a subgraph to a*planar*...*drawing**of*the whole*graph*-*and*the*simultaneous**planarity*problem-to find*planar**drawings**of*two*graphs*that coincide on shared vertices*and*edges. ... The authors would like to thank the anonymous referees for their useful comments*and*suggestions. ...##
###
Beyond-Planar Graphs: Algorithmics and Combinatorics (Dagstuhl Seminar 16452)

2017
*
Dagstuhl Reports
*

types

doi:10.4230/dagrep.6.11.35
dblp:journals/dagstuhl-reports/Hong0KP16
fatcat:gmft5jywxbapza52lhj4o23ngq
*of**crossings*, or*with*some forbidden*crossing*patterns. ... The common interest was in the exploration*of*structural properties*and*the development*of*algorithms for so-called beyond-*planar**graphs*, i.e., non-*planar**graphs**with*topological constraints such as specific ... RAC (*Right**Angle**Crossing*)*graphs*: a*graph*which has a straight-line*drawing**with**right**angle**crossings*. ...##
###
Drawing Subcubic 1-Planar Graphs with Few Bends, Few Slopes, and Large Angles
[article]

2018
*
arXiv
*
pre-print

We also show that 2 slopes always suffice for 1-

arXiv:1808.08496v1
fatcat:daio6jnv4fbw7avyy3olgt2g7e
*planar**drawings**of*subcubic 1-*planar**graphs**with*at most 2*bends*per edge. ... We show that the 1-*planar*slope number*of*3-connected cubic 1-*planar**graphs*is at most 4 when edges are drawn as polygonal curves*with*at most 1*bend*each. ... (3) Is the 1-*planar*slope number*of*1-*planar**graphs*bounded by a function*of*the maximum degree? ...##
###
Embedding Vertices at Points: Few Bends Suffice for Planar Graphs

2002
*
Journal of Graph Algorithms and Applications
*

We relax the latter requirement

doi:10.7155/jgaa.00046
fatcat:na25cjehenggzoi5exiboiom2a
*and*allow very*few**bends*on each edge while considering general plane*graphs*. ... Our results show two algorithms for mapping four-connected plane*graphs**with*at most one*bend*per edge*and*for mapping general plane*graphs**with*at most two*bends*per edge. ... Next we generalize the technique so that it will work for any*planar**graph**and*produces*drawings**with*at most two*bends*per edge. ...##
###
Embedding Vertices at Points: Few Bends Suffice for Planar Graphs
[chapter]

2004
*
Graph Algorithms and Applications 3
*

We relax the latter requirement

doi:10.1142/9789812796608_0005
fatcat:5mmbyksh7jerzdww3dkghbpdbi
*and*allow very*few**bends*on each edge while considering general plane*graphs*. ... Our results show two algorithms for mapping four-connected plane*graphs**with*at most one*bend*per edge*and*for mapping general plane*graphs**with*at most two*bends*per edge. ... Next we generalize the technique so that it will work for any*planar**graph**and*produces*drawings**with*at most two*bends*per edge. ...
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