Tutorial on Floorplan Representations Chungkuan Cheng Dept of

Tutorial on Floorplan Representations Chung-kuan Cheng Dept. of Computer Science and Engineering, University of California, San Diego La Jolla, CA 92093 -0404, USA

Outline Introduction l Types of Floorplans and Representations l Twin Binary Trees l Relations of Representations l Conclusions l

Introduction Foundation of Floorplanning Operations – Constructive Placement – Analytical Placement (QPlace) – Placement Perturbation (Annealing). l Description of Solution Domain l Engineering Change Order l

Types of Floorplans and Representations l l l 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

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

Twin Binary Trees Definition of Twin Binary Trees l Transformations between Floorplan and Twin Binary Trees l

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

Twin Binary Trees F C B A D F E B C 1 A E A D 0 X X X D E X 1 ( 1)=11001 F 0 0 1 B 1 C 0 ( 2)=00110 order( 1)=order( 2)=ABCDFE 0 1

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

TBT Relations B A X B A D F F C C E 0 1 0 order( 1)=order( 2)=ABCDFE 0 O-Tree 1 B F 0 1 D 0 X X X D 1 E A E C 1 B C A D F E SP 1=(ABCDFE, FADEBC) CBL=(FADEBC, 11101, 0010100) SP 2=(ABCDFE, FADBEC) CBL 90=(ABCDFE, 00110, 00101010)

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

Relations between Representations 900 SP (s 1, s 2) CBL (S, L, T) TBT ( +, -) O-tree T tree transform sequence

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