Filters








8,124 Hits in 8.3 sec

Area, Curve Complexity, and Crossing Resolution of Non-planar Graph Drawings [chapter]

Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta, Henk Meijer
2010 Lecture Notes in Computer Science  
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

Patrizio Angelini, Luca Cittadini, Walter Didimo, Fabrizio Frati, Giuseppe Di Battista, Michael Kaufmann, Antonios Symvonis
2011 Journal of Graph Algorithms and Applications  
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]

Patrizio Angelini, Luca Cittadini, Giuseppe Di Battista, Walter Didimo, Fabrizio Frati, Michael Kaufmann, Antonios Symvonis
2010 Lecture Notes in Computer Science  
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]

Kai Xu, Rohan Williams, Seok-Hee Hong, Qing Liu, Ji Zhang
2010 Lecture Notes in Computer Science  
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]

Michael T. Goodrich, Christopher G. Wagner
1998 Lecture Notes in Computer Science  
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

Michael T. Goodrich, Christopher G. Wagner
2000 Journal of Algorithms  
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]

David Eppstein, Michael T. Goodrich, Jeremy Yu Meng
2005 arXiv   pre-print
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]

Roberto Tamassia, Giuseppe Liotta
2004 Handbook of Discrete and Computational Geometry, Second Edition  
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]

Michael A. Bekos, Michael Kaufmann, Stephen G. Kobourov, Antonios Symvonis
2013 Lecture Notes in Computer Science  
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

Michael A. Bekos, Michael Kaufmann, Stephen G. Kobourov, Antonios Symvonis
2013 Journal of Graph Algorithms and Applications  
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]

David Eppstein, Michael T. Goodrich, Jeremy Yu Meng
2006 Lecture Notes in Computer Science  
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  
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)

Sok-Hee Hong, Michael Kaufmann, Stephen G. Kobourov, János Pach, Marc Herbstritt
2017 Dagstuhl Reports  
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]

Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani
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.  ...  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]

Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G. Kobourov, Martin Nöllenburg
2011 Lecture Notes in Computer Science  
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
« Previous Showing results 1 — 15 out of 8,124 results