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Area, Curve Complexity, and Crossing Resolution of Non-planar Graph Drawings
[chapter]
2010
Lecture Notes in Computer Science
Preserved Fulltext
In this paper we study non-planar 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 is worth mentioning that, if no requirement about the crossing resolution exists, then every planar graph admits a non-planar drawing in O(n) area [9] . ...
doi:10.1007/978-3-642-11805-0_4
fatcat:a56qxno5zfgffog2azbhy3m4ri
On the Perspectives Opened by Right Angle Crossing Drawings
2011
Journal of Graph Algorithms and Applications
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Third, we consider a natural non-planar generalization of planar embedded graphs. Here we give bounds for curve complexity and area different from the ones known for planar embeddings. ...
We prove that every graph with vertex-degree at most 6 (at most 3) admits a RAC drawing with curve complexity 2 (resp. 1) and with quadratic area. ...
We show that such graphs always admit RAC drawings with curve complexity 1 and that such a curve complexity is sometimes required. ...
doi:10.7155/jgaa.00217
fatcat:hhlcmlbxdfhl7fj2t5i3d4d3he
On the Perspectives Opened by Right Angle Crossing Drawings
[chapter]
2010
Lecture Notes in Computer Science
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Third, we consider a natural non-planar generalization of planar embedded graphs. Here we give bounds for curve complexity and area different from the ones known for planar embeddings. ...
We prove that every graph with vertex-degree at most 6 (at most 3) admits a RAC drawing with curve complexity 2 (resp. 1) and with quadratic area. ...
We show that such graphs always admit RAC drawings with curve complexity 1 and that such a curve complexity is sometimes required. ...
doi:10.1007/978-3-642-11805-0_5
fatcat:sdkmwoxbkjgm7kcm2sxqlvntuq
Semi-bipartite Graph Visualization for Gene Ontology Networks
[chapter]
2010
Lecture Notes in Computer Science
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Area, Curve Complexity, and Crossing Resolution of Non-Planar Graph Drawings Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta, and Henk Meijer Abstract: In this paper we study non-planar drawings of graphs ...
Third, we consider a natural non-planar generalization of planar embedded graphs. Here we give bounds for curve-complexity and area different from the ones known for planar embeddings. ...
doi:10.1007/978-3-642-11805-0_24
fatcat:724qxxufdzgthfzrovmnj4nzky
A Framework for Drawing Planar Graphs with Curves and Polylines
[chapter]
1998
Lecture Notes in Computer Science
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We describe a unified framework of aesthetic criteria and complexity measures for drawing planar graphs with polylines and curves. ...
and edge representational complexity and the area of the drawing. ...
For example, it seems that a drawing of a planar graph produced by this algorithm may have edge crossings. ...
doi:10.1007/3-540-37623-2_12
fatcat:k2yepvnn6vdchl2gzdbb6ppkcu
A Framework for Drawing Planar Graphs with Curves and Polylines
2000
Journal of Algorithms
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We describe a unified framework of aesthetic criteria and complexity measures for drawing planar graphs with polylines and curves. ...
and edge representational complexity and the area of the drawing. ...
For example, it seems that a drawing of a planar graph produced by this algorithm may have edge crossings. ...
doi:10.1006/jagm.2000.1115
fatcat:wbs2a25s5bbzvpbbkbgi7bodsa
Delta-confluent Drawings
[article]
2005
arXiv
pre-print
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We generalize the tree-confluent graphs to a broader class of graphs called Delta-confluent graphs. This class of graphs and distance-hereditary graphs, a well-known class of graphs, coincide. ...
Some results about the visualization of Delta-confluent graphs are also given. ...
One way to visualize a non-planar graph is to find a maximum planar subgraph of the original graph, compute a planar drawing of the subgraph, and add the rest of the original graph back on the drawing. ...
arXiv:cs/0510024v1
fatcat:z74wsvnuijglfhqac42jxbwd7i
Graph drawing
[chapter]
2004
Handbook of Discrete and Computational Geometry, Second Edition
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Bounds on geometric and topological properties of drawings (e.g., area and crossings) are presented in Section 1.2. Section 1.3 deals with the time complexity of fundamental graph drawing problems. ...
BOUNDS ON THE AREA
bound on the angular resolution of planar straight-line drawings of planar graphs. ...
doi:10.1201/9781420035315.ch52
fatcat:suzr5ked2veg7pmtmgpfppvrua
Smooth Orthogonal Layouts
[chapter]
2013
Lecture Notes in Computer Science
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We study the problem of creating smooth orthogonal layouts for planar graphs. ...
Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity-2 layout. The work of M.A. ...
Nöllenburg and I. Rutter for helpful discussions. ...
doi:10.1007/978-3-642-36763-2_14
fatcat:5zg4c4omgrekrmuocaklaaqxha
Smooth Orthogonal Layouts
2013
Journal of Graph Algorithms and Applications
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We study the problem of creating smooth orthogonal layouts for planar graphs. ...
Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity-2 layout. The work of M.A. ...
Nöllenburg and I. Rutter for helpful discussions. ...
doi:10.7155/jgaa.00305
fatcat:cpyhzz7ks5gqrim3xsxpu3nqpy
Delta-Confluent Drawings
[chapter]
2006
Lecture Notes in Computer Science
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We generalize the tree-confluent graphs to a broader class of graphs called ∆-confluent graphs. This class of graphs and distancehereditary graphs, a well-known class of graphs, coincide. ...
Some results about the visualization of ∆-confluent graphs are also given. ...
One way to visualize a non-planar graph is to find a maximum planar subgraph of the original graph, compute a planar drawing of the subgraph, and add the rest of the original graph back on the drawing. ...
doi:10.1007/11618058_16
fatcat:jc6se5vncvcszdiej5pzswonom
Page 6089 of Mathematical Reviews Vol. , Issue 2001I
[page]
2001
Mathematical Reviews
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and edge representational complexity and the area of the drawing. ...
Summary: “We describe a unified framework of aesthetic criteria and complexity measures for drawing planar graphs with poly- lines and curves. ...
Beyond-Planar Graphs: Algorithmics and Combinatorics (Dagstuhl Seminar 16452)
2017
Dagstuhl Reports
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The seminar brought together 29 researchers in the areas of graph theory, combinatorics, computational geometry, and graph drawing. ...
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 ...
Is it true that every graph of maximum degree ∆ = 3 (∆ = 4) admits a (non-geometric, that is, with curves) both quasi-planar and fan-crossing-free drawing? ...
doi:10.4230/dagrep.6.11.35
dblp:journals/dagstuhl-reports/Hong0KP16
fatcat:gmft5jywxbapza52lhj4o23ngq
A Survey on Graph Drawing Beyond Planarity
[article]
2018
arXiv
pre-print
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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. ...
On the other hand, if we insist in having a constant number of crossings per edge, planar and non-planar drawings of planar graphs have in general the same area requirement. ...
arXiv:1804.07257v1
fatcat:xeckxilhfbbgdbfhctikymlq6m
Lombardi Drawings of Graphs
[chapter]
2011
Lecture Notes in Computer Science
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We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs. ...
We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. ...
Non-Crossing Lombardi Drawings
Planar Graphs Without Planar Lombardi Drawings Not every planar graph has a planar Lombardi drawing. ...
doi:10.1007/978-3-642-18469-7_18
fatcat:jdtbo3ytbfamrnjmltfjs4e5a4
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