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Grid Drawings of Graphs with Constant Edge-Vertex Resolution
[article]

2021
*
arXiv
*
pre-print

We call such

arXiv:2005.02082v3
fatcat:2le2l2llqzgzxelzd7hl42kh5u
*drawings*disk-link*drawings*. In this paper we focus on the case*of**constant**edge*-*vertex**resolution*, namely ρ=1/2 (i.e., disks*of*unit diameter). ... We study the algorithmic problem*of*computing*drawings**of**graphs*in which (i) each*vertex*is a disk*with*fixed radius ρ, (ii) each*edge*is a straight-line segment connecting the centers*of*the two disks ... In relation to our work, they state that every 3-connected planar*graph**with*n vertices admits a convex*grid**drawing**with**constant**edge*-*vertex**resolution*in (3n − 7) × (3n − 7)/2 area. ...##
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Convex Grid Drawings of Planar Graphs with Constant Edge-Vertex Resolution
[article]

2022
*
arXiv
*
pre-print

We present a

arXiv:2204.14040v2
fatcat:mnpr6jdphzaxbpa4vshxdavthq
*drawing*algorithm that takes as input a 3-connected plane*graph**with*n vertices and f internal faces and computes a convex straight-line*drawing**with**edge*-*vertex**resolution*at least 1/2 on ...*edge*is lower bounded by a*constant*that does not depend on the size*of*the*graph*. ... A disk-link*drawing**of*a*graph*is a*grid**drawing**of**edge*-*vertex**resolution*at least 1 2 . ...##
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Limitations on Realistic Hyperbolic Graph Drawing
[article]

2021
*
arXiv
*
pre-print

We show that several types

arXiv:2108.07441v1
fatcat:dsvtulk42zevddres7vwvv2fg4
*of**graph**drawing*in the hyperbolic plane require features*of*the*drawing*to be separated from each other by sub-*constant*distances, distances so small that they can be accurately ... Therefore, for these types*of**drawing*, hyperbolic geometry provides no benefit over Euclidean*graph**drawing*. ...*Grid**graphs*also obey similar bounds (Theorem 5). -Beyond planar*graph**drawing*, every n-*vertex**graph*has a Euclidean*drawing**with*unit*vertex*-*vertex**resolution*and angular*resolution*Θ(1/n). ...##
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Convex drawings of graphs in two and three dimensions (preliminary version)

1996
*
Proceedings of the twelfth annual symposium on Computational geometry - SCG '96
*

We provide O(n)-time algorithms for constructing the following types

doi:10.1145/237218.237401
dblp:conf/compgeom/ChrobakGT96
fatcat:qxudyosndbbz5kll7ra2kdakku
*of**drawings**of*n-*vertex*3-connected planar*graphs*: 2D convex*grid**drawings**with*(3n) (3n=2) area under the*edge*L 1 -*resolution*rule ... ; 2D strictly convex*grid**drawings**with*O(n 3 ) O(n 3 ) area under the*edge**resolution*rule; 2D strictly convex*drawings**with*O(1) O(n) area under the*vertex*-*resolution*rule, and*with**vertex*coordinates ... Abstract We provide O(n)-time algorithms for constructing the following types*of**drawings**of*n-*vertex*3-connected planar*graphs*: 2D convex*grid**drawings**with*(3n) (3n=2) area under the*edge*L We also ...##
###
Drawing Planar Graphs with Circular Arcs
[chapter]

1999
*
Lecture Notes in Computer Science
*

In this paper we address the problem

doi:10.1007/3-540-46648-7_12
fatcat:myr7tfh3nvb4jftlljsxxszntm
*of**drawing*planar*graphs**with*circular arcs while maintaining good angular*resolution*and small*drawing*area. ... The algorithm runs in O(n) time and embeds the*graph*on the O(n) × O(n)*grid*, while maintaining Θ(1/d(v)) angular*resolution*, where d(v) is the degree*of**vertex*v. ... -We can*draw*an n-*vertex*planar*graph*G in an O(n)×O(n)*grid**with*angular*resolution*Θ (1/d(v) ) for each*vertex*v in G using at most two circular arcs per*edge*. ...##
###
Graph drawing
[chapter]

2004
*
Handbook of Discrete and Computational Geometry, Second Edition
*

*resolution*( ): smallest angle formed by two

*edges*, or segments

*of*

*edges*, incident on the same

*vertex*or bend, in a polyline

*drawing*. ... maxi- mum angular

*resolution*NP-hard 55, 73] embedded

*graph*test the existence

*of*a planar straight-line

*drawing*

*with*prescribed angles between pairs

*of*consecutive

*edges*incident on a

*vertex*NP-hard ...

##
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Optimal 3D Angular Resolution for Low-Degree Graphs

2013
*
Journal of Graph Algorithms and Applications
*

We show that every

doi:10.7155/jgaa.00290
fatcat:tzmzvdsapzfbxj2nbskewcl7cq
*graph**of*maximum degree four can be drawn in three dimensions*with*at most three bends per*edge*, and*with*109.5-degree angles, i.e., the angular*resolution**of*the diamond lattice, between ... We show that every*graph**of*maximum degree three can be drawn in three dimensions*with*at most two bends per*edge*, and*with*120-degree angles between any two*edge*segments meeting at a*vertex*or a bend ... This research was supported in part by the National Science Foundation under grant 0830403, by the Office*of*Naval Research under MURI grant N00014-08-1-1015, and by the German Research Foundation (DFG ...##
###
Optimal 3D Angular Resolution for Low-Degree Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

We show that every

doi:10.1007/978-3-642-18469-7_19
fatcat:mx4fphpq4bbz3mntenlkd6af7y
*graph**of*maximum degree four can be drawn in three dimensions*with*at most three bends per*edge*, and*with*109.5 • angles, i. e., the angular*resolution**of*the diamond lattice, between ... We show that every*graph**of*maximum degree three can be drawn in three dimensions*with*at most two bends per*edge*, and*with*120 • angles between any two*edge*segments meeting at a*vertex*or a bend. ... This research was supported in part by the National Science Foundation under grant 0830403, by the Office*of*Naval Research under MURI grant N00014-08-1-1015, and by the German Research Foundation (DFG ...##
###
Advances in the theory and practice of graph drawing

1999
*
Theoretical Computer Science
*

Foremost among the visual representations used are

doi:10.1016/s0304-3975(98)00272-2
fatcat:2ctscsnpxrg6zbu2cmcgo3raoi
*drawings**of**graphs*and ordered sets. In this talk, we survey recent advances in the theory and practice*of**graph**drawing*. ... The visualization*of*conceptual structures is a key component*of*support tools for complex applications in science and engineering. ... Some columns*of*the*grid*are "reserved" to*draw*the remaining incident*edges**of*v. ...##
###
Trade-Offs in Planar Polyline Drawings
[chapter]

2014
*
Lecture Notes in Computer Science
*

We present the first smooth tradeoff between the area and angular

doi:10.1007/978-3-662-45803-7_26
fatcat:ookdqvkasze5fpq7vs4gkpx5nq
*resolution*for 2-bend polyline*drawings**of*any given planar*graph*. ... Specifically, for any given n-*vertex*triangulation, our algorithm computes a*drawing**with*angular*resolution*r/d(v) at each*vertex*v, and area f (n, r), for any r ∈ (0, 1], where d(v) denotes the degree ... Allowing bends helps both to reduce area and to improve angular*resolution*, e.g., given an n-*vertex*planar*graph**with*maximum degree ∆, one can construct a 3-bend polyline*drawing**with*2/∆ radians*of**resolution*...##
###
Area, Curve Complexity, and Crossing Resolution of Non-planar Graph Drawings
[chapter]

2010
*
Lecture Notes in Computer Science
*

In this paper we study non-planar

doi:10.1007/978-3-642-11805-0_4
fatcat:a56qxno5zfgffog2azbhy3m4ri
*drawings**of**graphs*, 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, and the area. ... It would be interesting to study whether a o(n 2 ) area and good crossing*resolution*can be obtained for*graphs**with*O(n)*edges*. ...##
###
Small Area Drawings of Outerplanar Graphs
[chapter]

2006
*
Lecture Notes in Computer Science
*

On the other hand, the first algorithm constructs

doi:10.1007/11618058_9
fatcat:opwdgr4gx5abfasbv64nlxhvee
*drawings**with*better angular*resolution*. The third algorithm constructs outerplanar*drawings**of*general outerplanar*graphs**with*O(n 1.48 ) area. ... We show three linear time algorithms for constructing planar straightline*grid**drawings**of*outerplanar*graphs*. The first and the second algorithm are for balanced outerplanar*graphs*. ... We show (Section 3) a linear time algorithm for constructing nonouterplanar*drawings**of*balanced outerplanar*graphs*in linear area and*with*angular*resolution*≥ c √ n ,*with*c*constant*. ...##
###
A Framework for Drawing Planar Graphs with Curves and Polylines

2000
*
Journal of Algorithms
*

This framework includes several visual properties

doi:10.1006/jagm.2000.1115
fatcat:wbs2a25s5bbzvpbbkbgi7bodsa
*of*such*drawings*, including aspect ratio,*vertex**resolution*,*edge*length,*edge*separation, and*edge*curvature, as well as complexity measures such as*vertex*... More significantly, we show how to adapt this algorithm to*draw*any n-*vertex*planar*graph*using cubic Bézier curves,*with*all vertices and control points placed within an O(n) × O(n) integer*grid*so that ... One*of*the now-classic results for*drawing*planar*graphs*is an algorithm by de Fraysseix, Pach, and Pollack [3] for*drawing*an n-*vertex*planar*graph*in an O(n) × O(n) integer*grid*using straight line ...##
###
A Framework for Drawing Planar Graphs with Curves and Polylines
[chapter]

1998
*
Lecture Notes in Computer Science
*

This framework includes several visual properties

doi:10.1007/3-540-37623-2_12
fatcat:k2yepvnn6vdchl2gzdbb6ppkcu
*of*such*drawings*, including aspect ratio,*vertex**resolution*,*edge*length,*edge*separation, and*edge*curvature, as well as complexity measures such as*vertex*... More significantly, we show how to adapt this algorithm to*draw*any n-*vertex*planar*graph*using cubic Bézier curves,*with*all vertices and control points placed within an O(n) × O(n) integer*grid*so that ... One*of*the now-classic results for*drawing*planar*graphs*is an algorithm by de Fraysseix, Pach, and Pollack [3] for*drawing*an n-*vertex*planar*graph*in an O(n) × O(n) integer*grid*using straight line ...##
###
Polar Coordinate Drawing of Planar Graphs with Good Angular Resolution

2003
*
Journal of Graph Algorithms and Applications
*

In both algorithms we are concerned

doi:10.7155/jgaa.00073
fatcat:wnmyrz23sfeujico5hz4djmxwa
*with*the following*drawing*criteria: angular*resolution*, bends per*edge*,*vertex**resolution*, bend-point*resolution*,*edge*separation, and*drawing*area. ... We present a novel way to*draw*planar*graphs**with*good angular*resolution*. We introduce the polar coordinate representation and describe a family*of*algorithms for constructing it. ... Acknowledgments A preliminary version*of*this paper appeared in the Proceedings*of*the 9th Symposium on*Graph**Drawing*[4] . ...
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