## Orthogonal Grid Drawing of Clustered Graphs (1996)

Citations: | 4 - 2 self |

### BibTeX

@TECHREPORT{Eades96orthogonalgrid,

author = {Peter Eades and Qingwen Feng},

title = {Orthogonal Grid Drawing of Clustered Graphs},

institution = {},

year = {1996}

}

### OpenURL

### Abstract

Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal-grid rectangular cluster drawings. The drawing produced by the algorithm has constant number of bends on each edge and has O(n 2 ) area, which is as good as existing results for classical graph drawings. 1 Introduction Clustered graphs are graphs with recursive clustering structures over the vertices (see Fig. 1). This type of clustering structure appears in many systems. Examples include CASE tools [19], management information systems [10], and VLSI design tools [8]. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which ...

### Citations

543 | On Visual Formalisms
- Harel
- 1988
(Show Context)
Citation Context ...ring structures over the vertices (see Fig. 1). This type of clustering structure appears in many systems. Examples include CASE tools [19], management information systems [10], and VLSI design tools =-=[8]-=-. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. Algorithms for automatically draw... |

91 | Automatic graph drawing and readability of diagrams
- Tamassia, Battista
- 1988
(Show Context)
Citation Context ...gned, or we can say, single line segments. The next step is to construct orthogonal representation of the graph from the visibility representation. We only need to do some local operations similar to =-=[18]-=- for every vertex of G. These operations are illustrated in Fig. 5. Because of the cases shown in Fig. 5(f), (g), we need to reduce the length of the unit by half, or double the width of the drawing. ... |

69 |
Visualization of structural information: Automatic drawing of compound digraphs
- Sugiyama, Misue
- 1991
(Show Context)
Citation Context ...tains the drawing of all the vertices which belong to that cluster. Algorithms for automatically drawing of clustered graphs are difficult. Heuristic methods have been developed by Sugiyama and Misue =-=[17, 12]-=-, North [13], and by Madden et al. [16, 11]. Algorithms for constructing straight-line drawings of clustered graphs are given in [6, 4]; note, however, that straight-line drawings of clustered graphs ... |

62 |
Computing an st-numbering
- Even, Tarjan
- 1976
(Show Context)
Citation Context ...her-numbered vertex. Vertices s and t are called the source and the sink respectively. Such a numbering is an st numbering for G. An st numbering of a biconnected graph can be computed in linear time =-=[5]-=-. 3 n G( ) S T Figure 2: Illustration of Computing c-st Numbering and preserve the planar embedding in the meantime. The resulting graph is F (fl). Every vertex of F (fl) represents a child cluster of... |

61 | A better heuristic for orthogonal graph drawings
- Biedl, Kant
- 1998
(Show Context)
Citation Context ...ing. The algorithm runs in O(n) time and produces drawings within O(n 2 ) area and has constant number of bends on the drawing of each edge. This result is as good as the results for classical graphs =-=[3, 14, 9]-=-. For further development, some compaction techniques can be applied to improve the area performance of the algorithm. As presented in [6], a planar straight-line convex cluster drawing requires expon... |

59 |
R.: Algorithms for plane representations of acyclic digraphs
- Battista, Tamassia
- 1988
(Show Context)
Citation Context ...graph when drawing a c-planar clustered graph; and the embedding of the underlying graph G uniquely determines the embedding of the clustered graph. Our techniques use the concept of planar st-graphs =-=[1]-=-. A planar st-graph is a planar directed graph with one source s and one sink t; and both source and sink above can be embedded on the boundary of the same face, say the external face. 3 The Algorithm... |

58 | Straight-line drawing algorithms for hierarchical graphs and clustered graphs, in
- Eades, Feng, et al.
- 1996
(Show Context)
Citation Context ...t. Heuristic methods have been developed by Sugiyama and Misue [17, 12], North [13], and by Madden et al. [16, 11]. Algorithms for constructing straight-line drawings of clustered graphs are given in =-=[6, 4]-=-; note, however, that straight-line drawings of clustered graphs can require exponential area. In this paper, we present an algorithm which produce planar drawings of clustered graphs in a convention ... |

46 |
How to draw a planar clustered graph
- Feng, Cohen, et al.
- 1995
(Show Context)
Citation Context ...t. Heuristic methods have been developed by Sugiyama and Misue [17, 12], North [13], and by Madden et al. [16, 11]. Algorithms for constructing straight-line drawings of clustered graphs are given in =-=[6, 4]-=-; note, however, that straight-line drawings of clustered graphs can require exponential area. In this paper, we present an algorithm which produce planar drawings of clustered graphs in a convention ... |

29 |
The state of the art of visual languages for visualization
- Williams, Rasure, et al.
- 1992
(Show Context)
Citation Context ... 1 Introduction Clustered graphs are graphs with recursive clustering structures over the vertices (see Fig. 1). This type of clustering structure appears in many systems. Examples include CASE tools =-=[19]-=-, management information systems [10], and VLSI design tools [8]. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices... |

25 |
Drawing planar graphs using the canonical ordering, Algorithmica – Special Issue on Graph Drawing 16
- Kant
- 1996
(Show Context)
Citation Context ...ing. The algorithm runs in O(n) time and produces drawings within O(n 2 ) area and has constant number of bends on the drawing of each edge. This result is as good as the results for classical graphs =-=[3, 14, 9]-=-. For further development, some compaction techniques can be applied to improve the area performance of the algorithm. As presented in [6], a planar straight-line convex cluster drawing requires expon... |

13 |
Tollis, Constrained visibility representations of graphs
- Battista, Tamassia, et al.
- 1992
(Show Context)
Citation Context ...ed consecutively. With this c-st numbering, we transform a clustered graph into a planar-st graph by applying directions for edges of G according to the c \Gamma st numbering. We use the technique in =-=[2]-=- of producing visibility representations of planar stgraphs with some prespecified edges vertically aligned. A visibility representation \Gamma for a planar st-graph G maps each vertex v into a horizo... |

13 |
Drawing ranked digraphs with recursive clusters, in
- North
- 1993
(Show Context)
Citation Context ...g of all the vertices which belong to that cluster. Algorithms for automatically drawing of clustered graphs are difficult. Heuristic methods have been developed by Sugiyama and Misue [17, 12], North =-=[13]-=-, and by Madden et al. [16, 11]. Algorithms for constructing straight-line drawings of clustered graphs are given in [6, 4]; note, however, that straight-line drawings of clustered graphs can require ... |

13 |
Improved algorithms and bounds for orthogonal drawings
- Papakostas, Tollis
- 1995
(Show Context)
Citation Context ...ing. The algorithm runs in O(n) time and produces drawings within O(n 2 ) area and has constant number of bends on the drawing of each edge. This result is as good as the results for classical graphs =-=[3, 14, 9]-=-. For further development, some compaction techniques can be applied to improve the area performance of the algorithm. As presented in [6], a planar straight-line convex cluster drawing requires expon... |

10 |
KJ method: A scientific approach to problem solving
- Kawakita
- 1975
(Show Context)
Citation Context ...graphs with recursive clustering structures over the vertices (see Fig. 1). This type of clustering structure appears in many systems. Examples include CASE tools [19], management information systems =-=[10]-=-, and VLSI design tools [8]. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. Algori... |

9 |
An overview of diagram based idea organizer: D-ABDUCTOR
- Misue, Sugiyama
- 1993
(Show Context)
Citation Context ...tains the drawing of all the vertices which belong to that cluster. Algorithms for automatically drawing of clustered graphs are difficult. Heuristic methods have been developed by Sugiyama and Misue =-=[17, 12]-=-, North [13], and by Madden et al. [16, 11]. Algorithms for constructing straight-line drawings of clustered graphs are given in [6, 4]; note, however, that straight-line drawings of clustered graphs ... |

4 |
Methods for computer display and manipulation of graphs and the corresponding algorithms
- Read
- 1986
(Show Context)
Citation Context ...ces of the same cluster are numbered consecutively, we need to compute an ordering of the child clusters for every parent cluster . First, we triangulate G (including triangulating the external face) =-=[15]-=-. Therefore, the planar topology of the clustered graph is embedded in the graph. Then we construct a graph F () from G() by shrinking each child cluster ofsto a vertex while preserving the embedding.... |

3 |
Graph layout toolkit. available from bmadden @TomSawyer.COM
- Software
(Show Context)
Citation Context ... belong to that cluster. Algorithms for automatically drawing of clustered graphs are difficult. Heuristic methods have been developed by Sugiyama and Misue [17, 12], North [13], and by Madden et al. =-=[16, 11]-=-. Algorithms for constructing straight-line drawings of clustered graphs are given in [6, 4]; note, however, that straight-line drawings of clustered graphs can require exponential area. In this paper... |

2 |
Portable graph layout end editing
- Madden, Madden, et al.
(Show Context)
Citation Context ... belong to that cluster. Algorithms for automatically drawing of clustered graphs are difficult. Heuristic methods have been developed by Sugiyama and Misue [17, 12], North [13], and by Madden et al. =-=[16, 11]-=-. Algorithms for constructing straight-line drawings of clustered graphs are given in [6, 4]; note, however, that straight-line drawings of clustered graphs can require exponential area. In this paper... |