Corner Block List Representation and Its Application to Floorplan Optimization

1. Corner Block List Representation and Its Application to Floorplan Optimization Xianglong Hong Sheqin Dong Gang Huang Yici Cai Chung-Kuan Cheng Jun Gu IEEE 2004

2. Outline • Introduction • Preliminaries • Corner Block List (CBL) • Experimental Result • Conclusion

3. Introduction • VLSI floorplans are group into two categories - slicing structure - non-slicing structure • A floorplan devides the chip into rectangular rooms with horizontal and vertical segments. • The internal segments intersect and form T- junctions.

4. Preliminaries • Mosaic floorplan : covers slicing floorplans and a subset of non-slicing floorplans. • Definition: 1) Floorplan of n rooms: each room is assigned one and only one block. 2) Topological equivalence on segment sliding : the topology is defined to be equivalent before and after the non-crossing segment of T-junction slides. 3) Non-degenerate topology : there is no degenerate case where toe distinct T-junctions meet at the same point.

5. (a) (b) topological equivalence

6. Constraint Graph G(V,E) , where the nodes in V represent separating segment , and the directed edges in E represent the rectangular rooms. • Two kinds of constraint graphs: - horizontal constraint graph (HCG) - vertical constraint graph (VCG)

7. Corner Edges : an edge that is incident to an east (E) or north (N) pole. • Corner Block : the block whose two constraint edges are corner edges in both HCG and VCG.

8. Orientation of corner block : define the orientation of a corner block according to the bottom left corner T-junction of its room. • 1) vertical oriented : use 0 to record oriented. T-junction is rotated by 90o counterclockwise. • 2) horizontal oriented : use 1 to record oriented. T-junction is rotated by 180o counterclockwise. 1

9. Corner block deletion • If the corner block is horizontaloriented 1) delete the corner block 2) shift its left segment to the right boundary and pull the attached T-junctions along with the segment. • If the corner block isverticaloriented 1) delete the corner block 2) shift its bottom segment to the top boundary and pull up the attached T-junctions along with the segment.

10. Operate the corner block deletion on the constraint graph: 1) remove its corresponding edges in HCG and VCG. 2) if the corner block is vertical oriented, we merge the source node of its constraint edge and the north pole in VCG. if the corner block is horizontal oriented, merge the source node of its constraint edge and the east pole in HCG.

11. 1

12. Corner block insertion : the inverse of the deletion. - If the inserted corner block is vertical oriented, push down the horizontal segment from the top . - If the inserted corner block is horizontal oriented, push left the vertical segment from the right. • The constraint graph is recovered accordingly.

13. insert d vertical

14. T i -> 00…01 S 7 = d L 7 = 0 T 7 = 01 k (input number) Corner Block List (CBL) • The CBL is recorded from a series of corner block deletions. • For i th block deletion, record a block name Bi, orientation Li and the binary string Ti.

15. At the end of deletion iterations, obtain three list : 1) block name list : Bn, Bn-1,…,B1 2) oriented list : Ln ,Ln-1,…,L2 3) T-binary-string list: Tn, Tn-1, …, T2 • Keep the CBL(S,L,T) in a reversed order. i.e., S = B1 ,B2 ,….,Bn L = L2 , … , Ln-1 , Ln T = T2 , …, Tn-1 , Tn

16. b b b b b a a a a a c c c c c d d d d d a c d c d c B 4 = b L 4 = 1 T 4 = 1 B 3 = a L 3 = 0 T 3 = 01 (S , L , T ) S = c d a b L = 1 0 1 T = 1 01 1 B 2 = d L 2 = 1 T 2 = 1 B 1 = c

19. Using simulated annealing process. • Objective function: • Six operation:

20. Experimental Results • Implement in the C programming language on a SUN SPAR 2000 workstation.

22. Conclusion • In this paper, CBL can not only represent all floorplans with slicing structure, but also represent floorplans with non-slicing structrue. • CBL can be extended to represent this situation by allowing empty room,present in [11], [12].