## A Simple Linear Time Algorithm for Proper Box Rectangular Drawing of Plane Graphs (2000)

Venue: | Journal of Algorithms |

Citations: | 6 - 0 self |

### BibTeX

@ARTICLE{He00asimple,

author = {Xin He},

title = {A Simple Linear Time Algorithm for Proper Box Rectangular Drawing of Plane Graphs},

journal = {Journal of Algorithms},

year = {2000},

volume = {40},

pages = {40--1}

}

### OpenURL

### Abstract

In this paper we introduce a new drawing style of a plane graph G, called proper box rectangular (PBR ) drawing. It is defined to be a drawing of G such that every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal or a vertical line segment, and each face is drawn as a rectangle. We establish necessary and sufficient conditions for G to have a PBR drawing. We also give a simple linear time algorithm for finding such drawings. The PBR drawing is closely related to the box rectangular (BR ) drawing defined by Rahman, Nakano and Nishizeki [17]. Our method can be adapted to provide a new simpler algorithm for solving the BR drawing problem. 1 Introduction The problem of "nicely" drawing a graph G has received increasing attention [5]. Typically, we want to draw the edges and the vertices of G on the plane so that certain aesthetic quality conditions and/or optimization measures are met. Such drawings are very useful in visualizing planar graphs and fi...

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Citation Context ...gular drawing, and (d) a box-rectangular drawing. drawn as a rectangle as illustrated in Fig 1 (c). Since rectangular drawings have applications in VLSI floorplanning, it has been extensively studied =-=[11, 13, 14, 22]-=-. Not every plane graph has a rectangular drawing. Necessary and sufficient conditions for G to have such a drawing were given in [23]. Several linear time algorithms for constructing such drawings ar... |

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Citation Context ...izeki [17]. Our method can be adapted to provide a new simpler algorithm for solving the BR drawing problem. 1 Introduction The problem of "nicely" drawing a graph G has received increasing =-=attention [5]-=-. Typically, we want to draw the edges and the vertices of G on the plane so that certain aesthetic quality conditions and/or optimization measures are met. Such drawings are very useful in visualizin... |

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Citation Context ...nimation and so on. Among different drawing styles, an orthogonal drawing has attracted much attention due to its applications in circuit layouts, database diagrams, entity-relationship diagrams etc. =-=[4, 9, 19, 20, 21]-=-. In an orthogonal drawing of a plane graph G, each vertex is drawn as an integer grid point and each edge is drawn as a sequence of alternate horizontal and vertical line segments along grid lines as... |

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Citation Context ...nimation and so on. Among different drawing styles, an orthogonal drawing has attracted much attention due to its applications in circuit layouts, database diagrams, entity-relationship diagrams etc. =-=[4, 9, 19, 20, 21]-=-. In an orthogonal drawing of a plane graph G, each vertex is drawn as an integer grid point and each edge is drawn as a sequence of alternate horizontal and vertical line segments along grid lines as... |

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Citation Context ...ery plane graph has a rectangular drawing. Necessary and sufficient conditions for G to have such a drawing were given in [23]. Several linear time algorithms for constructing such drawings are known =-=[2, 8, 10, 16]-=-. As it can be easily seen, a box-orthogonal drawing is a generalization of an orthogonal drawing which in turn is a generalization of a rectangular drawing. Thus, an orthogonal drawing is an intermed... |

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Citation Context ...s generating excessive heat should not be adjacent, or two modules operating on high frequency should not be adjacent to avoid interference [17, 18]. Another example is in architectural floorplanning =-=[7]-=-: in a chemical plant, a processing unit that deals with poisonous chemical should not be adjacent to a cafeteria. The unwanted adjacency can be avoided if we use the BR drawing instead of the rectang... |

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Citation Context ...ery plane graph has a rectangular drawing. Necessary and sufficient conditions for G to have such a drawing were given in [23]. Several linear time algorithms for constructing such drawings are known =-=[2, 8, 10, 16]-=-. As it can be easily seen, a box-orthogonal drawing is a generalization of an orthogonal drawing which in turn is a generalization of a rectangular drawing. Thus, an orthogonal drawing is an intermed... |

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Citation Context ...ery plane graph has a rectangular drawing. Necessary and sufficient conditions for G to have such a drawing were given in [23]. Several linear time algorithms for constructing such drawings are known =-=[2, 8, 10, 16]-=-. As it can be easily seen, a box-orthogonal drawing is a generalization of an orthogonal drawing which in turn is a generalization of a rectangular drawing. Thus, an orthogonal drawing is an intermed... |

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Citation Context ...A box-orthogonal drawing is a natural generalization of an orthogonal drawing. Every plane graph has a box-orthogonal drawing even if its maximum degree iss5. The box-orthogonal drawing is studied in =-=[3, 6, 15]-=-. An orthogonal drawing of a plane graph G is called a rectangular drawing if each edge of G is drawn as a straight line seqment without bends and the contour of each face of G is 1 (a) (b) (c) (d) Fi... |

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Citation Context ...n VLSI floorplanning, it has been extensively studied [11, 13, 14, 22]. Not every plane graph has a rectangular drawing. Necessary and sufficient conditions for G to have such a drawing were given in =-=[23]-=-. Several linear time algorithms for constructing such drawings are known [2, 8, 10, 16]. As it can be easily seen, a box-orthogonal drawing is a generalization of an orthogonal drawing which in turn ... |

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Citation Context ...e a PBR drawing. We also give a simple linear time algorithm for finding such drawings. The PBR drawing is closely related to the box rectangular (BR ) drawing defined by Rahman, Nakano and Nishizeki =-=[17]. Our meth-=-od can be adapted to provide a new simpler algorithm for solving the BR drawing problem. 1 Introduction The problem of "nicely" drawing a graph G has received increasing attention [5]. Typic... |

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Citation Context ...gular drawing, and (d) a box-rectangular drawing. drawn as a rectangle as illustrated in Fig 1 (c). Since rectangular drawings have applications in VLSI floorplanning, it has been extensively studied =-=[11, 13, 14, 22]-=-. Not every plane graph has a rectangular drawing. Necessary and sufficient conditions for G to have such a drawing were given in [23]. Several linear time algorithms for constructing such drawings ar... |

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Citation Context ...gular drawing, and (d) a box-rectangular drawing. drawn as a rectangle as illustrated in Fig 1 (c). Since rectangular drawings have applications in VLSI floorplanning, it has been extensively studied =-=[11, 13, 14, 22]-=-. Not every plane graph has a rectangular drawing. Necessary and sufficient conditions for G to have such a drawing were given in [23]. Several linear time algorithms for constructing such drawings ar... |

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Citation Context ...nimation and so on. Among different drawing styles, an orthogonal drawing has attracted much attention due to its applications in circuit layouts, database diagrams, entity-relationship diagrams etc. =-=[4, 9, 19, 20, 21]-=-. In an orthogonal drawing of a plane graph G, each vertex is drawn as an integer grid point and each edge is drawn as a sequence of alternate horizontal and vertical line segments along grid lines as... |

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Citation Context ...A box-orthogonal drawing is a natural generalization of an orthogonal drawing. Every plane graph has a box-orthogonal drawing even if its maximum degree iss5. The box-orthogonal drawing is studied in =-=[3, 6, 15]-=-. An orthogonal drawing of a plane graph G is called a rectangular drawing if each edge of G is drawn as a straight line seqment without bends and the contour of each face of G is 1 (a) (b) (c) (d) Fi... |

6 | Orthogonal drawing of high degree graphs with small area and few bends
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Citation Context ...A box-orthogonal drawing is a natural generalization of an orthogonal drawing. Every plane graph has a box-orthogonal drawing even if its maximum degree iss5. The box-orthogonal drawing is studied in =-=[3, 6, 15]-=-. An orthogonal drawing of a plane graph G is called a rectangular drawing if each edge of G is drawn as a straight line seqment without bends and the contour of each face of G is 1 (a) (b) (c) (d) Fi... |

1 |
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