## An Exact Rectilinear Steiner Tree Algorithm (1993)

Venue: | In Proceedings of the International Conference on Computer Design |

Citations: | 15 - 6 self |

### BibTeX

@INPROCEEDINGS{Salowe93anexact,

author = {J. S. Salowe and D. M. Warme},

title = {An Exact Rectilinear Steiner Tree Algorithm},

booktitle = {In Proceedings of the International Conference on Computer Design},

year = {1993},

pages = {472--475}

}

### OpenURL

### Abstract

Given a set of terminals in the plane, a rectilinear Steiner minimal tree is a shortest interconnection among these terminals using only horizontal and vertical edges. We present an algorithm that constructs a rectilinear Steiner minimal tree for an input terminal set. On a workstation, problems involving 20 input terminals can be solved in a few seconds, and problems involving 30 input terminals can be solved, on average, in 30 minutes. Previous algorithms could only solve 16 or 17 point problems within the 30 minute time bound. 1 Introduction Let V be a set of n points in the plane called terminals. A rectilinear Steiner minimal tree for V is a tree of shortest length containing V as its vertex set, where the distance between two vertices is measured in the rectilinear metric. Rectilinear Steiner minimal trees are useful in VLSI physical design, particularly global routing and wire-length estimation. Garey and Johnson[3] showed that the decision problem corresponding to the rectili...

### Citations

357 |
The Steiner Tree Problem
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- 1992
(Show Context)
Citation Context ... then the circumrectangle of fa; b; cg must be empty. 3.2 Large Cardinality Restrictions In 1976, Hwang[4] showed that full topologies have a restrictive structure, given below. (Refer to Hwang et al.=-=[5]-=- for undefined notation.) Theorem 3 (Hwang) Let jV j = n ? 4, and suppose that V is a full set. Then there is a rectilinear Steiner minimal tree for V consisting of either (1) a complete line with n \... |

105 |
On Steiner Minimal Trees with Rectilinear Distance
- Hwang
- 1976
(Show Context)
Citation Context ...its relative interior. Theorem 2 Let a; b; c 2 V . If fa; b; cg is a full set with respect to V , then the circumrectangle of fa; b; cg must be empty. 3.2 Large Cardinality Restrictions In 1976, Hwang=-=[4]-=- showed that full topologies have a restrictive structure, given below. (Refer to Hwang et al.[5] for undefined notation.) Theorem 3 (Hwang) Let jV j = n ? 4, and suppose that V is a full set. Then th... |

96 | A new class of iterative Steiner tree heuristics with good performance
- Kahng, Robins
- 1992
(Show Context)
Citation Context ...e rectilinear Steiner minimal trees for smallsized terminals sets. The second is a comparison of the exact solution to Steiner tree heuristics, particularly the 1-Steiner heuristic of Kahng and Robins=-=[6]-=-. It turns out that, up to 30 input terminals, 1-Steiner is typically within 0:5% of optimal. The reader is directed to Section 5 for details on both contributions. Our algorithm was inspired and infl... |

36 |
The Rectilinear Steiner Problem is NP-Complete
- Garey, Johnson
- 1977
(Show Context)
Citation Context ...ween two vertices is measured in the rectilinear metric. Rectilinear Steiner minimal trees are useful in VLSI physical design, particularly global routing and wire-length estimation. Garey and Johnson=-=[3]-=- showed that the decision problem corresponding to the rectilinear Steiner minimal tree problem is NP-complete; even though NP-completeness strongly suggests this problem has no polynomial-time soluti... |

13 | Rectilinear Steiner Tree Minimization on a Workstation," Computational Support for Discrete
- Thomborson, Alpern, et al.
- 1994
(Show Context)
Citation Context ...lgorithms in the literature are only applicable to problems containing up to roughly 17 points. (See Yang and Wing[11], Sidorenko[8], Lewis, Pong, and Van Cleave[7], and Thomborson, Alpern, and Carter=-=[9]-=-.) From the standpoint of VLSI design, there are two important contributions of this work. The first is the design and construction of a tool that can efficiently compute rectilinear Steiner minimal t... |

13 |
An algorithm for the Steiner problem in the Euclidean plane
- Winter
- 1985
(Show Context)
Citation Context ...t terminals, 1-Steiner is typically within 0:5% of optimal. The reader is directed to Section 5 for details on both contributions. Our algorithm was inspired and influenced by recent results of Winter=-=[10]-=- and Cockayne and Hewgill[2] on exact algorithms for Euclidean Steiner minimal trees. These algorithms, as well as our own, focus on full topologies and full sets. Full topologies are Steiner minimal ... |

11 |
Optimal and suboptimal solution algorithms for the wiring problem
- Yang, Wing
- 1972
(Show Context)
Citation Context ...describe and study an algorithm that is effective on 30 input terminals. The fastest algorithms in the literature are only applicable to problems containing up to roughly 17 points. (See Yang and Wing=-=[11]-=-, Sidorenko[8], Lewis, Pong, and Van Cleave[7], and Thomborson, Alpern, and Carter[9].) From the standpoint of VLSI design, there are two important contributions of this work. The first is the design ... |

5 |
On minimal rectilinear Steiner trees
- Sidorenko
- 1989
(Show Context)
Citation Context ...udy an algorithm that is effective on 30 input terminals. The fastest algorithms in the literature are only applicable to problems containing up to roughly 17 points. (See Yang and Wing[11], Sidorenko=-=[8]-=-, Lewis, Pong, and Van Cleave[7], and Thomborson, Alpern, and Carter[9].) From the standpoint of VLSI design, there are two important contributions of this work. The first is the design and constructi... |

2 |
Hewgill, "Exact computation of Steiner minimal trees in the plane
- Cockayne, E
- 1986
(Show Context)
Citation Context ...ep 1. The output is a subset of these full sets from which a rectilinear Steiner minimal tree can be extracted. This procedure is essentially a rectilinear analogue of the work of Cockayne and Hewgill=-=[1, 2]-=-. In order to find a Steiner minimal tree, the candidate full topologies must be combined. The resulting object must contain all terminals in V , and it must correspond to a tree of shortest length. I... |

2 |
Hewgill, "Improved computation of plane Steiner minimal trees," Algorithmica 7
- Cockayne, E
- 1992
(Show Context)
Citation Context ...ically within 0:5% of optimal. The reader is directed to Section 5 for details on both contributions. Our algorithm was inspired and influenced by recent results of Winter[10] and Cockayne and Hewgill=-=[2]-=- on exact algorithms for Euclidean Steiner minimal trees. These algorithms, as well as our own, focus on full topologies and full sets. Full topologies are Steiner minimal trees, all of whose terminal... |

2 |
Cleave, "Optimum Steiner tree generation
- Lewis, Pong, et al.
- 1992
(Show Context)
Citation Context ...ve on 30 input terminals. The fastest algorithms in the literature are only applicable to problems containing up to roughly 17 points. (See Yang and Wing[11], Sidorenko[8], Lewis, Pong, and Van Cleave=-=[7]-=-, and Thomborson, Alpern, and Carter[9].) From the standpoint of VLSI design, there are two important contributions of this work. The first is the design and construction of a tool that can efficientl... |