## Randomized Graph Drawing with Heavy-Duty Preprocessing (1994)

Venue: | In: AVI ’94: Proceedings of the Workshop on Advanced Visual Interfaces |

Citations: | 14 - 1 self |

### BibTeX

@ARTICLE{Harel94randomizedgraph,

author = {David Harel and Meir Sardas},

title = {Randomized Graph Drawing with Heavy-Duty Preprocessing},

journal = {In: AVI ’94: Proceedings of the Workshop on Advanced Visual Interfaces},

year = {1994},

volume = {6},

pages = {233--253}

}

### Years of Citing Articles

### OpenURL

### Abstract

: We present a graph drawing system for general undirected graphs with straight-line edges. It carries out a rather complex set of preprocessing steps, designed to produce a topologically good, but not necessarily nice-looking layout, which is then subjected to Davidson and Harel's simulated annealing beautification algorithm. The intermediate layout is planar for planar graphs and attempts to come close to planar for nonplanar graphs. The system's results are significantly better, and much faster, than what the annealing approach is able to achieve on its own. 1 Introduction A large amount of work on the problem of graph layout has been carried out in recent years, resulting in a number of sophisticated and powerful algorithms. An extensive and detailed survey can be found in [BETT93]. Many of the approaches taken are limited to special cases of graphs, such as trees or planar graphs; others concentrate on special kinds of layouts, such as rectilinear grid drawings, or convex drawin...

### Citations

575 | On Visual Formalisms
- Harel
- 1988
(Show Context)
Citation Context ...vs. planarity. 8 Future work Clearly, much remains to be done. Some topics that pertain to harder problems (e.g., richer graphical objects, such as curved-line graphs, hypergraphs [Ber73] or higraphs =-=[Har88]-=-) were alluded to in [DH89]. Some work on hypergraphs has already been done; see [BETT93]. However, even in the more humble realm of straight-line graphs, the present paper, although improving [DH89],... |

544 | A framework for dynamic graph drawing - Cohen, Battista, et al. - 1992 |

528 |
Graphs and Hypergraphs
- Berge
- 1973
(Show Context)
Citation Context ...Figure 14: Symmetry vs. planarity. 8 Future work Clearly, much remains to be done. Some topics that pertain to harder problems (e.g., richer graphical objects, such as curved-line graphs, hypergraphs =-=[Ber73]-=- or higraphs [Har88]) were alluded to in [DH89]. Some work on hypergraphs has already been done; see [BETT93]. However, even in the more humble realm of straight-line graphs, the present paper, althou... |

521 | An algorithm for drawing general undirected graphs - Kamada, Kawai |

485 | Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-tree Algorithms - Booth, Lueker - 1976 |

191 | Drawing Graphs Nicely Using Simulated Annealing
- Davison, Harel
- 1996
(Show Context)
Citation Context ...raphs, such as trees or planar graphs; others concentrate on special kinds of layouts, such as rectilinear grid drawings, or convex drawings. In this paper, we continue the work of Davidson and Harel =-=[DH89], which ad-=-dresses the general problem of drawing arbitrary undirected graphs on the plane, with edges drawn as straight-line segments. The goal is to try to achieve as "nice" a drawing as possible. Pa... |

112 |
A linear algorithm for embedding planar graphs using PQ-trees
- Chiba, Nishizeki, et al.
- 1985
(Show Context)
Citation Context ... we carry out the following: Phase A: Planarity testing. Phase B: Planar embedding. Phase C: Planar drawing. Phase D: Randomized beautification. Phase B uses the PQ-trees-based algorithm presented in =-=[CNAO85]-=- to construct a planar embedding, i.e., an ordered list of the neighbors of each vertex, which, if layed out appropriately in cyclic order around the vertex, leads to a planar drawing. Phase C then us... |

106 | An algorithm for planarity testing of graphs - Lempel, Even, et al. - 1966 |

46 |
Small sets supporting Fáry embeddings of planar graphs
- Fraysseix, Pach, et al.
- 1988
(Show Context)
Citation Context ...a possible planar drawing of G. Our algorithm is a generalized version of the drawing algorithm of Chrobak and Payne [CP90], which, in turn, is based on an algorithm by de Fraysseix, Pach and Pollack =-=[FPP88]-=-. This algorithm draws a graph with n vertices on a grid of size (2n \Gamma 4) \Theta (n \Gamma 2); vertices are placed on grid points and edges 2 We thus call this part of our system the randomized p... |

25 | O(n 2 ) algorithms for graph planarization - Jayakumar, Thulasiraman, et al. - 1989 |

20 |
A linear time algorithm for drawing a planar graph on a grid
- Chrobak, Payne
- 1990
(Show Context)
Citation Context ...x, with v's list containing the edges incident to it in circular order around v in a possible planar drawing of G. Our algorithm is a generalized version of the drawing algorithm of Chrobak and Payne =-=[CP90]-=-, which, in turn, is based on an algorithm by de Fraysseix, Pach and Pollack [FPP88]. This algorithm draws a graph with n vertices on a grid of size (2n \Gamma 4) \Theta (n \Gamma 2); vertices are pla... |

17 | An O(n2) maximal planarization algorithm based on PQ-trees - Kant - 1992 |

1 |
Tollis, "Algorithms for Automatic Graph Drawing: An Annotated Bibliogra24 phy
- Battista, Eades, et al.
- 1993
(Show Context)
Citation Context ...ge amount of work on the problem of graph layout has been carried out in recent years, resulting in a number of sophisticated and powerful algorithms. An extensive and detailed survey can be found in =-=[BETT93]-=-. Many of the approaches taken are limited to special cases of graphs, such as trees or planar graphs; others concentrate on special kinds of layouts, such as rectilinear grid drawings, or convex draw... |

1 |
An Incremental Drawing Algorithm for Planar Graphs", in preparation
- Harel, Sardas
(Show Context)
Citation Context ...planar graphs, the phases are as follows: 1 This is the most technicaly involved part of our work, and we have devoted a separate paper to the detailed description and analysis of this algorithm; see =-=[HS93]-=-. 2 Phase A: Planarity testing. Phase B \Gamma : Extracting planar subgraph. Phase B: Planar embedding. Phase B + : Reinserting removed edges. Phase C: Planar drawing. Phase D 0 : Extended randomized ... |

1 |
A New Method for Drawing a Planar Graph Given the Order of Edges at Each Vertex
- Read
- 1987
(Show Context)
Citation Context ...me for triangulation, we have to be able to check the existence of an edge in constant time. This can be done by using an n \Theta n adjacency matrix to represent the graph, and a method suggested in =-=[Rea87]-=- to avoid the quadratic time that zeroing the matrix at the initialization stage would take.(However, this requires quadratic space.) Thus, the method that emerges is to (i) triangulate the graph, (ii... |

1 | Drawing Graphs Nicely on the Plane", M.Sc - Sardas - 1993 |