Floorplanning using a tree representation

Pei Ning Guo, Toshihiko Takahashi, Chung Kuan Cheng, Takeshi Yoshimura

Research output: Contribution to journal › Article

71 Citations (Scopus)

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!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.

Original languageEnglish
Pages (from-to)281-289
Number of pages9
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Volume20
Issue number2
DOIs
Publication statusPublished - 2001 Feb
Externally publishedYes

Fingerprint

Binary trees
Program processors
Wire

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

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

In: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 20, No. 2, 02.2001, p. 281-289.

Research output: Contribution to journal › Article

Guo, PN, Takahashi, T, Cheng, CK & Yoshimura, T 2001, 'Floorplanning using a tree representation', 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
Guo PN, Takahashi T, Cheng CK, Yoshimura T. Floorplanning using a tree representation. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 2001 Feb;20(2):281-289. https://doi.org/10.1109/43.908471
Guo, Pei Ning ; Takahashi, Toshihiko ; Cheng, Chung Kuan ; Yoshimura, Takeshi. / Floorplanning using a tree representation. In: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 2001 ; Vol. 20, No. 2. pp. 281-289.
@article{fd6bf1030a3b478caaab210eb6297e25,
title = "Floorplanning using a tree representation",
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!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.",
keywords = "Building block placement, Floorplan, Rooted ordered tree",
author = "Guo, {Pei Ning} and Toshihiko Takahashi and Cheng, {Chung Kuan} and Takeshi Yoshimura",
year = "2001",
month = "2",
doi = "10.1109/43.908471",
language = "English",
volume = "20",
pages = "281--289",
journal = "IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems",
issn = "0278-0070",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
number = "2",

}

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 -

Access to Document