## 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 |
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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 |

## 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