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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 92093-0404,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 Types of Floorplans 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 #slicing floorplan is 2 Schrőder number. A B C D E F A B C D E F Slicing Ordered Tree colors of adj. nodes differ

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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 0 90 0 180 0 270 0 C + -neighbor: 0 0 T-junction, block on right 270 0 T-junction, block on top C - -neighbor: 90 0 T-junction, block on top 180 0 T-junction, block on left A B0 A B 270 0 A B 90 0 A B 180 0

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A B C D E F C B A E D F X 1 1 0 0 1 X X X 0 1 0 1 0 F A D B C E Twin Binary Trees ( 1 )=11001 ( 2 )=00110 order( 1 )=order( 2 )=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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A B C D E F F C B A E D F X 1 1 0 0 1 X X X 0 1 0 1 0 A D B C E order( 1 )=order( 2 )=ABCDFE Relations TBT A B C D E F O-Tree SP1=(ABCDFE,FADEBC) SP2=(ABCDFE,FADBEC) CBL=(FADEBC,11101,0010100) CBL90=(ABCDFE,00110,00101010)

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Relations between Representations(mosaic) 1. TBT( +, - ): SP(s 1, s 2 ), s.t. order ( +) = s 1. 2. TBT( +, - ): CBL (S,L,T) 90, order ( + ) = S. 3. CBL(S,L,T): SP(s 1, s 2 ), s.t. s 2 = S. 4. TBT( +, - ): O-tree T, s.t. - = binary tree transformation(T)

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Relations between Representations CBL (S,L,T) TBT ( +, - ) O-tree T SP (s 1,s 2 ) 90 0 sequence tree transform

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

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