1. The Early Days of Automatic Floorplan Design
Martin D.F. Wong
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
ISPD 2016

2. Floorplan Design Pack modules on a rectangular chip to optimize total
area and interconnect cost.
Module:
– Hard modules
– Soft modules C B A D
Connectivity: A B C D 2 1 10 5

3. Early 1980s Min-Cut Placement Rectangular Dual Slicing Structure
U. Lauther, “A min-cut placement algorithm for general cell assemblies based on a graph representation”, DAC 1979.
Rectangular Dual
W. Heller, G. Sorkin, K. Maling, “The planar package planner for system designers”, DAC 1982.
Slicing Structure
R. Otten, “Automatic Floorplan Design”, DAC 1982.
R. Otten, “Efficient Floorplan Optimization”, ICCD 1983.
L. van Ginneken and R. Otten, “Optimal slicing of plane point placement”, Euro-DAC 1990.
Simulated Annealing
S. Kirpatrick, C. Gellat, M. Vechhi, “Optimization by Simulated Annealing”, Science 1983.
R. Otten and L. van Ginneken, “Floorplan Design using Annealing”, ICCAD 1984
C. Sechen and A. Sangiovanni-Vicentelli, “The Timberwolf Placement and Routing Package”, IEEE Journal on Solid State Circuits, April 1985.
D. F. Wong and C. L. Liu, “A new algorithm for floorplan design”, DAC 1986.

4. Min-Cut Placement (Lauther 79)
Polar graph placement data structure
Series-parallel graphs
Placement optimization
Minimize
Minimize

5. Polar Graphs Series-parallel graphs for min-cut placement. v1 v2 v3 v46 2 5 4 3 7 1 2 5 7 4 3 6 v1 v2 v4 v3 v5 h1 h2 h3 h4 h5 h1 h2 h3 h4 h5 1 2 3 4 5 6 7

6. Rectangular Dual
Heller, Sorkin, Maling 1982 1 2 5 4 3
Rectangular floorplan
Rectangular Dual Graph (RDG) 3 4 5 1 2 1 2 5 4 3

7. Rectangular Dual 1 2 5 4 3 RDG represents module adjacenciesb a
No floorplan exists 1 2 5 4 3
Rectangular floorplan
Rectangular Dual Graph (RDG) 3 4 5 1 2 3 4 5 1 2
triangles
RDG represents module adjacencies
Assume no cross junction, a RDG is a planar triangulated graph
No complex triangle

8. Slicing Structure R. Otten, “Automatic Floorplan Design”, DAC 1982 3 24 5 V H 6 7 6 7 1 5 2 3 4
Slicing Floorplan
Slicing Tree

9. Otten’s Approach (1982 DAC)
Convert net weights into “distances” (Dutch metric)
Analytically place n points in a suitable high dimensional space to exactly match these “distances”.
Project all points onto a 2-dimensional space with guaranteed minimum error.
Recursively slice the 2D points into two parts to derive a slicing structure consistent with the ordering of the points.
How to slice?
Determine shrink factor for each slice line.
Determine deformation factor for each slice line.
Pick the slice line with largest shrink factor s.t. deformation is within a given value.

10. d(i,j) d(i,j) = 1- cij Point Placement Dutch Metric Deformation Factor2
d(i,j) = 1- cij
Deformation Factor

11. Shrinking Factor

12. Optimal Slicing of Plane Point Placement
L. van Ginneken and R. Otten, Euro-DAC 1990
Dynamic Programming
Find shape curve for this
rectangle over all possible
slicing structures

13. Optimal Slicing of Plane Point Placements
Otten, 1983 ICCD

14. Other Applications
Mehta, Chen, Menezes, Wong, Pillegi, “Clustering and load balancing for
buffered clock tree synthesis”, ICCD 1997.
Wu, Wong, Liu, “Post-Placement voltage island generation under performance
Requirement”, ICCAD 2005.

15. Simulated Annealing * + 2 3 * 1 + 4 5 + 6 7 * + * 3 2 1 4 5 6 7
Wong and Liu, DAC 1986 6 7 1 5 2 3
Slicing Tree 4
Slicing Floorplan
2 3 * * + *
Polish Expression
DAC-86

16. DAC-86

17. Wong-Liu Algorithm
DAC-86

18. Wong-Liu Algorithm
DAC-86

19. How good are slicing floorplans?

20. Results for Soft Blocks
Experimental results => slicing is good for soft modules
*all modules have aspect ratio between 0.5 and 2

21. Results for Hard Blocks
Excellent results by slicing for the largest MCNC benchmarks (Cheng, Deng, Wong, ASPDAC 2005)

22. Results on Large Benchmarks
Yan and Chu, DAC-2008
Slicing approach produced best results on GSRC & HB large benchmarks 22

23. Can we mathematically explain these excellent empirical results?

24. Theoretical Analysis Theorem [Young and Wong ISPD-97]
Given a set of soft blocks of total area Atotal , maximum area
Amax and shape flexibility r  2, there exists a slicing floorplan
F of these blocks such that:
where

25. Can we do better?
Conjecture: For each non-slicing floorplan, there exists a slicing floorplan with “similar” area and topology.
Are slicing floorplans
“dense” ?
slicing floorplan

26. Wheel Floorplans with Squared Blocks
Lemma Given any wheel floorplan with 5 squared blocks, there is a “neighboring” slicing floorplan with equal/smaller area.
It is not possible that x1 > x2 and x2 > x3 and x3 > x4 and x4 > x1. Otherwise, x1 > x1!
We may assume x1 ≤ x2. It is easy to see that there is a “neighboring” slicing floorplan which is smaller!

27. Tightly Packed Wheel Floorplans
5 blocks: A, B, C, and D are identical; E is a square
0 ≤ x ≤ 1; block aspect ratio is in [1/2,2]
When 0 ≤ x < 0.783
There is a neighboring slicing floorplan with area at most 1.77% larger

28. Tightly Packed Wheel Floorplans
When ≤ｘ≤ 1
The neighboring slicing floorplan can be packed with zero dead-space

29. Slicing Tree is a “Complete” Floorplan Representation
Theorem (Lai & Wong, DATE 2001)
Each slicing tree gives a maximally compact placement
Conversely, each maximally compact placement can be obtained from a slicing tree 3 2 1 4 5 * + 6 7 1 2 6 5 3 4 1 2 6 5 3 4 7 7

30. Conclusions
Presented a brief survey of floorplan design work in early 1980s.
Prof. Otten’s work had great impact on the early part of my career.
Congratulations on the ISPD Life Time Achievement Award!