## Constraints in graph drawing algorithms (1998)

Venue: | Constraints |

Citations: | 15 - 0 self |

### BibTeX

@ARTICLE{Tamassia98constraintsin,

author = {Roberto Tamassia},

title = {Constraints in graph drawing algorithms},

journal = {Constraints},

year = {1998},

volume = {3},

pages = {87--120}

}

### Years of Citing Articles

### OpenURL

### Abstract

Abstract. Graphs are widely used for information visualization purposes, since they provide a natural and intuitive representation of complex abstract structures. The automatic generation of drawings of graphs has applications a variety of fields such as software engineering, database systems, and graphical user interfaces. In this paper, we survey algorithmic techniques for graph drawing that support the expression and satisfaction of user-defined constraints. 1.

### Citations

1405 | Network flows: theory, algorithms, and applications - Ahuja, Magnanti, et al. - 1993 |

515 | A heuristic for graph drawing
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Citation Context ...ergy configuration of the physical system. Forcedirected methods are referred in the literature also as spring methods and physical simulation methods. 2.1. Spring Embedder In Eades’ spring embedder (=-=Eades, 1984-=-), every pair of vertices is connected by a “spring”: • for adjacent vertices, the spring has unit natural length, thus attracting the vertices unless they are at the “ideal” unit distance;also, the s... |

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208 |
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Citation Context ...s algorithm have been been widely used in information visualization applications. 3.1. Planarization Methods Finding the minimum number of crossings or a maximum planar subgraph are NP-hard problems (=-=Garey and Johnson, 1983-=-). Hence, existing planarization algorithms use heuristics. A simple planarization method that uses as a subroutine an algorithm for finding a planar subgraph works as follows (see Fig. 6): 1. compute... |

130 |
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(Show Context)
Citation Context ...ssing with a fictitious vertex, and then a drawing method for planar graphs is applied (see Fig. 5). A successful drawing algorithm based on the planarization approach and a bend-minimization method (=-=Tamassia, 1987-=-) (see Section 6) is described in Tamassia, Di Battista, and Batini (1988). Systems based on this algorithm have been been widely used in information visualization applications. 3.1. Planarization Met... |

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(Show Context)
Citation Context ... displacement parameter. 2.2. Other Force-Directed Methods The force-directed approach was pioneered in Eades (1984), Kruskal and Seery (1980). Notable developments include Davidson and Harel (1996), =-=Frick, Ludwig, and Mehldau, 1995-=-), Fruchterman and Reingold (1991), Harel and Sardas (1995), Kamada and Kawai (1989), Sugiyama and Misue (1995). In particular:sCONSTRAINTS IN GRAPH DRAWING ALGORITHMS 91 (a) (c) Figure 2. Simulation ... |

91 | Automatic graph drawing and readability of diagrams - Tamassia, Battista - 1988 |

82 |
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(Show Context)
Citation Context ...time are given in Di Battista and Tamassia (1988), Rosenstiehl and Tarjan (1986), Tamassia and Tollis (1986). Algorithm 4.2 (Visibility) (Di Battista and Tamassia, 1988; Rosenstiehl and Tarjan, 1986; =-=Tamassia and Tollis, 1986-=-) provides a direct construction of a visibility representation for a planar st-graph G. For the sake of simplicity, the same notation is used for a vertex-segment of the visibility representation and... |

81 |
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(Show Context)
Citation Context ...structed by the barycentric method. The barycentric equations form a linear system whose known values are the x- and y-coordinates of the vertices of cycle γ . Tutte proved the following deep result (=-=Tutte, 1960-=-; Tutte 1963) (see Fig. 4): THEOREM 1 For a planar triconnected graph G, the barycentric equations admit a unique solution that yields a planar straight-line drawing of G such that the external face i... |

76 | Planar Graphs: Theory and Algorithms - Nishizeki, Chiba - 1988 |

66 |
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(Show Context)
Citation Context ...ity representations in linear time are given in Di Battista and Tamassia (1988), Rosenstiehl and Tarjan (1986), Tamassia and Tollis (1986). Algorithm 4.2 (Visibility) (Di Battista and Tamassia, 1988; =-=Rosenstiehl and Tarjan, 1986-=-; Tamassia and Tollis, 1986) provides a direct construction of a visibility representation for a planar st-graph G. For the sake of simplicity, the same notation is used for a vertex-segment of the vi... |

59 | R.: Algorithms for plane representations of acyclic digraphs - Battista, Tamassia - 1988 |

56 |
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Citation Context ...proposed by Cruz and Garg (1995). Within this approach, a graph is stored in an object-oriented database, and its drawing is visually defined using recursive rules of the visual meta-language DOODLE (=-=Cruz, 1992-=-). The application of the visual rules to the input graph yields a system of constraints that can be solved in linear time for the following types of drawings: • layered drawings and box inclusion dra... |

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22 |
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(Show Context)
Citation Context ...d Lin (1995) attempt at combining algorithmic and constraintbased declarative methods in drawings of trees, and Brandenburg presents a comprehensive approach to graph drawing based on graph grammars (=-=Brandenburg, 1995-=-), where drawings are generated by rule-based methods. 8. Visual Graph Drawing A visual approach to graph drawing, where the layout of a graph is pictorially specified “by example,” is proposed by Cru... |

19 |
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(Show Context)
Citation Context ...ed visual organization features. The first method is rule-based and implemented in Prolog. The second method is a genetic algorithm to be executed by a massively parallel computer. The third, method (=-=Dengler, Friedell, and Marks, 1993-=-) incrementally improves an initial randomly-generated drawing using a force-directed technique, and is the most practical. This approach has also been used within an interactive graph drawing system ... |

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16 | A new minimum cost flow algorithm with applications to graph drawing
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(Show Context)
Citation Context ...anti, and Orlin (1993). It runs in time T(n) = O(n 2 log n) using O(n) space. A more complex algorithm, which exploits the sparsity of network N , runs in time T(n) = O(n 7/4 log n) using O(n) space (=-=Garg and Tamassia, 1997-=-). 2 2 4 4s112 R. TAMASSIA 4 14 4 1 2 3 Figure 17. Example of flow φ associated with a planar orthogonal representation (drawn with dashed lines). Only the arcs with nonzero flow are shown. The thickn... |

15 | Constraint-Based Spring-Model Algorithm for Graph Layout - Kamps, Kleinz, et al. |

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14 | Graph Drawing
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(Show Context)
Citation Context ... Orlin (1993). It runs in time T(n) = O(n 2 log n) using O(n) space. A more complex algorithm, which exploits the sparsity of network N , runs in time T(n) = O(n 7/4 log n) using O(n) space (Garg and =-=Tamassia, 1997-=-). 2 2 4 4s112 R. TAMASSIA 4 14 4 1 2 3 Figure 17. Example of flow φ associated with a planar orthogonal representation (drawn with dashed lines). Only the arcs with nonzero flow are shown. The thickn... |

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13 |
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(Show Context)
Citation Context ...e for the source vertex; (c) rule for a vertex; (d) rule for an edge. • polyline drawings (Di Battista and Tamassia, 1988), visibility drawings (Tamassia and Tollis, 1986), and tessellation drawings (=-=Tamassia and Tollis, 1989-=-) of upward planar digraphs. Complete visual programs for visibility representations and upward polyline drawings are shown in Figures 20 and 21, respectively. We assume that the vertices, edges, and ... |

6 | K.: Graph drawing by magnetic-spring model - Sugiyama, Misue - 1995 |

5 | An approach to automatic display layout using combinatorial optimization algorithms - Luders, Ernst, et al. - 1995 |

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(Show Context)
Citation Context ... incrementally improves an initial randomly-generated drawing using a force-directed technique, and is the most practical. This approach has also been used within an interactive graph drawing system (=-=Ryall, Marks, and Shieber, 1997-=-). Luders et al. (1995) present a combinatorial approach for satisfying inequality constraints between vertex coordinates within a graph drawing system. Kamps et al. (1996) show how to extend force-di... |

3 | A formal specification for network diagrams that facilitates automated design - Marks - 1991 |

2 | Data Structures and Algorithms, Volumes 1--3 - Mehlhorn - 1984 |

1 | Special issue on Graph Drawing, edited by - Algorithmica - 1989 |

1 | Special issue on Graph Visualization, edited by - Tamassia - 1985 |