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**Tutorial on Floorplan Representations**

Chung-kuan Cheng Dept. of Computer Science and Engineering, University of California,San Diego La Jolla,CA ,USA

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**Outline Introduction Types of Floorplans and Representations**

Twin Binary Trees Relations of Representations Conclusions

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**Introduction Foundation of Floorplanning Operations**

Constructive Placement Analytical Placement (QPlace) Placement Perturbation (Annealing). Description of Solution Domain Engineering Change Order

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**Types of Floorplans and Representations**

Floorplan Representations Slicing Floorplan: Slicing Order Tree Mosaic Floorplan: Corner Block List General Floorplan: Sequence Pair, O-Tree Combinations of Floorplans and Representations

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**Slicing Floorplan Slicing floorplan Slicing ordered tree**

B C D E F Slicing Ordered Tree colors of adj. nodes differ A B C D E F Slicing floorplan Slicing ordered tree #slicing floorplan is 2 Schrőder number.

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**Twin Binary Trees Definition of Twin Binary Trees**

Transformations between Floorplan and Twin Binary Trees

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Twin Binary Trees T T T T 00 900 1800 2700 C+-neighbor: 00 T-junction, block on right 2700 T-junction, block on top A B 2700 A B 00 C--neighbor: 900 T-junction, block on top 1800 T-junction, block on left A B 900 A B 1800

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**Twin Binary Trees C E B B C A A D D E F F X 1 (1)=11001 (2)=00110**

A B C D E F (1)=11001 (2)=00110 order(t1)=order(t2)=ABCDFE

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**Twin Binary Trees and Mosaic Floorplan**

Twin Binary Tree Mosaic Floorplan : one to one mapping Transformation between twin binary trees and mosaic floorplan takes linear complexity #twin binary trees = Baxter number

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**Relations F TBT C B A E D F X 1 order(t1)=order(t2)=ABCDFE A B C D E F**

order(t1)=order(t2)=ABCDFE A B C D E F O-Tree A B C D E F CBL=(FADEBC,11101, ) CBL90=(ABCDFE,00110, ) SP1=(ABCDFE,FADEBC) SP2=(ABCDFE,FADBEC)

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**Relations between Representations(mosaic)**

TBT(t+,t-): SP(s1, s2), s.t. order (t+) = s1. 2. TBT(t+,t-): CBL (S,L,T)90, order (t+) = S. 3. CBL(S,L,T): SP(s1, s2), s.t. s2= S. 4. TBT(t+,t-): O-tree T, s.t. t- = binary tree transformation(T)

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**Relations between Representations**

CBL (S,L,T) TBT (t+,t-) O-tree T SP (s1,s2) 900 sequence tree transform

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**{slicing fps} {mosaic fps} {general fps} **

Conclusion {slicing fps} {mosaic fps} {general fps} #slicing O-trees #TBTs #SPs #O-trees O-tree rep. one of TBTs * block sizes A B C Mixed mode floorplan, mixed signal floorplan. Interconnect planning.

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