### Abstract

We present an ordered tree (O tree) structure to represent nonslicing floorplans. The O tree uses only n(2 + [lg n]) bits for a floorplan of n rectangular blocks. We define an admissible placement as a compacted placement in both x and y directions. For each admissible placement, we can find an O-tree representation. We show that the number of possible O-tree combinations is O(n!2^{2n-2}/n^{1.5}). This is very concise compared to a sequence pair representation that has O((n!)^{2}) combinations. The approximate ratio of sequence pair and O-tree combinations is O(n^{2}(n/4e)^{n}). The complexity of O tree is even smaller than a binary tree structure for slicing floorplan that has O(n!2^{5n-3}/n^{1.5}) combinations. Given an O tree, it takes only linear time to construct the placement and its constraint graph. We have developed a deterministic floorplanning algorithm utilizing the structure of O tree. Empirical results on MCNC (www.mcnc.org) benchmarks show promising performance with average 16% improvement in wire length and 1% less dead space over previous central processing unit (CPU) intensive cluster refinement method.

Original language | English |
---|---|

Pages (from-to) | 281-289 |

Number of pages | 9 |

Journal | IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems |

Volume | 20 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2001 Feb |

Externally published | Yes |

### Fingerprint

### Keywords

- Building block placement
- Floorplan
- Rooted ordered tree

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Hardware and Architecture
- Computer Science Applications
- Computational Theory and Mathematics

### Cite this

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*,

*20*(2), 281-289. https://doi.org/10.1109/43.908471

**Floorplanning using a tree representation.** / Guo, Pei Ning; Takahashi, Toshihiko; Cheng, Chung Kuan; Yoshimura, Takeshi.

Research output: Contribution to journal › Article

*IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems*, vol. 20, no. 2, pp. 281-289. https://doi.org/10.1109/43.908471

}

TY - JOUR

T1 - Floorplanning using a tree representation

AU - Guo, Pei Ning

AU - Takahashi, Toshihiko

AU - Cheng, Chung Kuan

AU - Yoshimura, Takeshi

PY - 2001/2

Y1 - 2001/2

N2 - We present an ordered tree (O tree) structure to represent nonslicing floorplans. The O tree uses only n(2 + [lg n]) bits for a floorplan of n rectangular blocks. We define an admissible placement as a compacted placement in both x and y directions. For each admissible placement, we can find an O-tree representation. We show that the number of possible O-tree combinations is O(n!22n-2/n1.5). This is very concise compared to a sequence pair representation that has O((n!)2) combinations. The approximate ratio of sequence pair and O-tree combinations is O(n2(n/4e)n). The complexity of O tree is even smaller than a binary tree structure for slicing floorplan that has O(n!25n-3/n1.5) combinations. Given an O tree, it takes only linear time to construct the placement and its constraint graph. We have developed a deterministic floorplanning algorithm utilizing the structure of O tree. Empirical results on MCNC (www.mcnc.org) benchmarks show promising performance with average 16% improvement in wire length and 1% less dead space over previous central processing unit (CPU) intensive cluster refinement method.

AB - We present an ordered tree (O tree) structure to represent nonslicing floorplans. The O tree uses only n(2 + [lg n]) bits for a floorplan of n rectangular blocks. We define an admissible placement as a compacted placement in both x and y directions. For each admissible placement, we can find an O-tree representation. We show that the number of possible O-tree combinations is O(n!22n-2/n1.5). This is very concise compared to a sequence pair representation that has O((n!)2) combinations. The approximate ratio of sequence pair and O-tree combinations is O(n2(n/4e)n). The complexity of O tree is even smaller than a binary tree structure for slicing floorplan that has O(n!25n-3/n1.5) combinations. Given an O tree, it takes only linear time to construct the placement and its constraint graph. We have developed a deterministic floorplanning algorithm utilizing the structure of O tree. Empirical results on MCNC (www.mcnc.org) benchmarks show promising performance with average 16% improvement in wire length and 1% less dead space over previous central processing unit (CPU) intensive cluster refinement method.

KW - Building block placement

KW - Floorplan

KW - Rooted ordered tree

UR - http://www.scopus.com/inward/record.url?scp=0035248720&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035248720&partnerID=8YFLogxK

U2 - 10.1109/43.908471

DO - 10.1109/43.908471

M3 - Article

VL - 20

SP - 281

EP - 289

JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

SN - 0278-0070

IS - 2

ER -