## Compact Floor-Planning via Orderly Spanning Trees

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Venue: | J. Algorithms |

Citations: | 15 - 1 self |

### BibTeX

@ARTICLE{Liao_compactfloor-planning,

author = {Chien-Chih Liao and Hsueh-i Lu and Hsu-Chun Yen},

title = {Compact Floor-Planning via Orderly Spanning Trees},

journal = {J. Algorithms},

year = {},

volume = {48},

pages = {441--451}

}

### Years of Citing Articles

### OpenURL

### Abstract

Floor-planning is a fundamental step in VLSI chip design. Based upon the concept of orderly spanning trees, we present a simple O(n)-time algorithm to construct a oorplan for any n-node plane triangulation. In comparison with previous oor-planning algorithms in the literature, our solution is not only simpler in the algorithm itself, but also produces oor-plans which require fewer module types. An equally important aspect of our new algorithm lies in its ability to t the oor-plan area in a rectangle of size (n 1) . Lower bounds on the worst-case area for oor-planning any plane triangulation are also provided in the paper.

### Citations

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Citation Context ...ed upon a recent development of orderly spanning trees [4], which provides an extension of canonical ordering [7, 12, 13] to plane graphs not required to be triconnected and an extension for realizer =-=[19, 20]-=- to plane graphs not required to be triangulated. Our approach bypasses the somewhat complicated rectangular-dual phase. Aside from the two applications of orderly spanning trees reported in [4] (name... |

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Citation Context ...algorithm to construct a floor-plan of a plane triangulation using only 2-rectangular modules. He’s floor-planning algorithms consists of three phases: The first phase utilizes the canonical ordering =-=[6,11,12]-=- to assign nodes on separating triangles. The second phase involves the socalled vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms [1,2,8... |

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Citation Context ...sses the somewhat complicated rectangular-dual phase. Aside from the two applications of orderly spanning trees reported in [4] (namely, succinct encodings for planar graphs with ecient query support =-=[5, 11, 18-=-] and 2-visibility drawings for planar graphs [8]), our investigation heresnds another interesting application of orderly spanning trees. (A similar concept called ordered stratication and its applica... |

67 | Drawing planar graphs using the canonical ordering
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Citation Context ...algorithm to construct a floor-plan of a plane triangulation using only 2-rectangular modules. He’s floor-planning algorithms consists of three phases: The first phase utilizes the canonical ordering =-=[6,11,12]-=- to assign nodes on separating triangles. The second phase involves the socalled vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms [1,2,8... |

64 |
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Citation Context ...rtime algorithm to construct asoor-plan of a plane triangulation using only 2-rectangular modules. He'ssoor-planning algorithms consists of three phases: Thesrst phase utilizes the canonical ordering =-=[7, 12, 13]-=- to assign nodes on separating triangles. The second phase involves the so-called vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms [1, 2... |

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Citation Context ...rtime algorithm to construct asoor-plan of a plane triangulation using only 2-rectangular modules. He'ssoor-planning algorithms consists of three phases: Thesrst phase utilizes the canonical ordering =-=[7, 12, 13]-=- to assign nodes on separating triangles. The second phase involves the so-called vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms [1, 2... |

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Citation Context ...ed upon a recent development of orderly spanning trees [4], which provides an extension of canonical ordering [7, 12, 13] to plane graphs not required to be triconnected and an extension for realizer =-=[19, 20]-=- to plane graphs not required to be triangulated. Our approach bypasses the somewhat complicated rectangular-dual phase. Aside from the two applications of orderly spanning trees reported in [4] (name... |

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Citation Context ...`(j) and j = r(i) holds. The concept of orderly spanning tree for plane graphs [4] extends that of canonical orderings[7, 12, 13] for plane graphs not required to be triconnected and that of realizer =-=[6, 19, 20-=-] for plane graphs not required to be triangulated. Specically, when G is a plane triangulation, (i) if T is an orderly spanning tree of G, then the counterclockwise preordering of the nodes of T is a... |

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Citation Context ...ost worst-case optimal. What \simplicity" means is two-fold: First, as opposed to the multiple-phase approach of [10, 23], our algorithm is based upon a recent development of orderly spanning tr=-=ees [4]-=-, which provides an extension of canonical ordering [7, 12, 13] to plane graphs not required to be triconnected and an extension for realizer [19, 20] to plane graphs not required to be triangulated. ... |

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Citation Context ...11,12] to assign nodes on separating triangles. The second phase involves the socalled vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms =-=[1,2,8,12]-=- to finalize the drawing of the floor-plan. Figure 2 depicts the shapes of the 2-rectangular modules required by He’s algorithm. For convenience, these four shapes are referred to as I-module, L-modul... |

25 |
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Citation Context ...rtime algorithm to construct asoor-plan of a plane triangulation using only 2-rectangular modules. He'ssoor-planning algorithms consists of three phases: Thesrst phase utilizes the canonical ordering =-=[7, 12, 13]-=- to assign nodes on separating triangles. The second phase involves the so-called vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms [1, 2... |

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Citation Context ...11,12] to assign nodes on separating triangles. The second phase involves the socalled vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms =-=[1,2,8,12]-=- to finalize the drawing of the floor-plan. Figure 2 depicts the shapes of the 2-rectangular modules required by He’s algorithm. For convenience, these four shapes are referred to as I-module, L-modul... |

20 |
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Citation Context ...16] that a plane triangulation G admits a rectangular dual if and only if G has four exterior nodes, and G has no separating triangles. (A separating triangle, which is also known as complex triangle =-=[22, 23]-=-, is a cycle of three edges enclosing some nodes in its interior.) As forsoor-planning general plane graphs, Yeap and Sarrafzadeh [23] showed that rectilinear modules with at most two concave corners ... |

17 |
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Citation Context ...s drawn in dark. The node labels show the counterclockwise preordering of the nodes in T . (b) Asoor-plan of G. (a) (b) (c) (d) Figure 2: Four types of modules required by He'ssoor-planning algorithm =-=[10]-=-: (a) I-module, (b) L-module, (c) T-module, and (d) Z-module. Our algorithm does not need Z-modules. In a subsequent study ofsoor-planning, He [10] measured the complexity of a module in terms of the ... |

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11 |
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Citation Context ..., 13] to assign nodes on separating triangles. The second phase involves the so-called vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms =-=[1, 2, 9, 13]-=- tosnalize the drawing of thesoorplan. Figure 2 depicts the shapes of the 2-rectangular modules required by He's algorithm. For convenience, these four shapes are referred to as I-module, L-module, T-... |

10 |
2-visibility drawings of planar graphs
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Citation Context ...ide from the two applications of orderly spanning trees reported in [4] (namely, succinct encodings for planar graphs with ecient query support [5, 11, 18] and 2-visibility drawings for planar graphs =-=[8-=-]), our investigation heresnds another interesting application of orderly spanning trees. (A similar concept called ordered stratication and its application in constructing 2-visibility drawing were i... |

9 |
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Citation Context ... a rectangle of size (n 1) 2n+1 3 . Lower bounds on the worst-case area forsoor-planning any plane triangulation are also provided in the paper. 1 Introduction In VLSI chip design,soor-planning [17=-=, 22]-=- refers to the process of, given a graph whose nodes (respectively, edges) representing functional entities (respectively, interconnections), partitioning a rectangular chip area into a set of non-ove... |

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7 |
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Citation Context ... a rectangle of size (n 1) 2n+1 3 . Lower bounds on the worst-case area forsoor-planning any plane triangulation are also provided in the paper. 1 Introduction In VLSI chip design,soor-planning [17=-=, 22]-=- refers to the process of, given a graph whose nodes (respectively, edges) representing functional entities (respectively, interconnections), partitioning a rectangular chip area into a set of non-ove... |

6 | Floorplanning by graph dualization: L-shaped modules - Sun, Sarrafzadeh - 1993 |

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5 | 2-visibility drawings of planar graphs
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Citation Context ...de from the two applications of orderly spanning trees reported in [3] (namely, succinct encodings for planar graphs with efficient query support [4,10,17] and 2-visibility drawings for planar graphs =-=[7]-=-), our investigation here finds another interesting application of orderly spanning trees. • Second, the floor-plan design of our algorithm is “simpler” (in comparison with [9]) in its own right, in t... |

4 | Orthogonal drawings based on the stratification of planar graphs. Discrete Mathematics
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Citation Context ...cation of orderly spanning trees. (A similar concept called ordered stratification and its application in constructing 2-visibility drawing were independently studied by Bonichon, Le Saëc, and Mosbah =-=[21]-=-.) • Second, the floor-plan design of our algorithm is “simpler” (in comparison with [3]) in its own right, in the sense that I-modules, L-modules, and T-modules suffice. (Recall that Z-modules are ne... |

2 |
A linear algorithm to a rectangular dual of a planar triangulated graph. Algorithmica
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(Show Context)
Citation Context ..., 13] to assign nodes on separating triangles. The second phase involves the so-called vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms =-=[1, 2, 9, 13]-=- tosnalize the drawing of thesoorplan. Figure 2 depicts the shapes of the 2-rectangular modules required by He's algorithm. For convenience, these four shapes are referred to as I-module, L-module, T-... |

2 |
On the rectangular duals of planar triangular graphs
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(Show Context)
Citation Context ..., 13] to assign nodes on separating triangles. The second phase involves the so-called vertex expansion operation to break all separating triangles. The third phase adapts rectangular-dual algorithms =-=[1, 2, 9, 13]-=- tosnalize the drawing of thesoorplan. Figure 2 depicts the shapes of the 2-rectangular modules required by He's algorithm. For convenience, these four shapes are referred to as I-module, L-module, T-... |

2 |
2-visibility drawings of planar graphs, in: S. North (Ed
- Fößmeier, Kant, et al.
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(Show Context)
Citation Context ...ide from the two applications of orderly spanning trees reported in [14] (namely, succinct encodings for planar graphs with efficient query support [17–19] and 2-visibility drawings for planar graphs =-=[20]-=-), our investigation here finds another interesting application of orderly spanning trees. (A similar concept called ordered stratification and its application in constructing 2-visibility drawing wer... |

1 |
Orthogonal drawings based on the strati cation of planar graphs
- Bonichon, Saec, et al.
(Show Context)
Citation Context ...cation of orderly spanning trees. (A similar concept called ordered stratication and its application in constructing 2-visibility drawing were independently studied by Bonichon, Le Saec, and Mosbah [3=-=].) -=-Second, thesoor-plan design of our algorithm is \simpler" (in comparison with [10]) in its own right, in the sense that I-modules, L-modules, and T-modules suce. (Recall that Z-modules are needed... |