1. Constrained ‘Modern’ Floorplanning
Yan Feng
Dinesh P. Mehta
Colorado School of Mines
Hannah Yang
Intel

2. Motivation/Assumption
Fixed die formulation with zero whitespace .
(A. B. Kahng, ISPD 2000)
Modules shapes need not be restricted to rectangles, L-shapes, etc. (A. B. Kahng, ISPD 2000)
Approximate locations and sizes for modules are already known from quadratic placement, force-directed placement, or human design.
1)The boundary is fixed
2) In other words ,the shape could be rectilinear polygon
3) Either from previous step or from the architect experience, the location and size of each module are already known

3. Proposed Design Flow Input No Make suggestions Bound-Feasible
to make input
feasible No
Bound-Feasible
Yes
Min Cost Max Flow
Based Floorplanner
1) Animation to show this paper’s work
Postprocessing Step No
Connected?
Yes

4. The Constrained Modern Floorplanning Problem(CMFP)
Module
Center W H
Required Area A
(30,30) 60
2500 B
(75,50) 50
100
4000 C
(50,75)
100 50
3500
(0,0)
(100,100) A B C
(0,0)
(100,100) A B C
The CMFP problem is NP-hard.

5. Feasibility Analysis Area(BC) = 8000 A B Required(BC) = 8500 C
Module
Center W H
Required Area A
(30,30) 60
2500 B
(75,50) 50
100
4000 C
(50,75)
4500

6. Feasibility Analysis A B C D E Center Area W H A (50,50) 8000 100 B
(0,0) A B C D E
Center
Area W H A
(50,50)
8000
100 B
(135,55)
12000
130
110 C
(235,45)
10000 90 D
(75,145)
150 E
(220,125)
18000
160
(300,200)

7. Region Identification3 4 11 10 5 12 15 C A 2 7 B 1 6 9 14 E 13 D

8. Flow-based Feasibility Analysis
If the maximum network flow of graph is equal to the total required area of modules then the input is feasible.

9. Experiment result (ami 33)
How do you get the input of ami33?

10. Floorplanning
The result of Max Flow algorithm does not guarantee connectivity.
Min Cost Max Flow Problem: each edge also has a cost a(u,v). So if f(u,v) units flow over edge (u,v), we incur a cost of a(u,v)f(u,v).
Computes a maximum flow as before, but finds one of min cost.
Post Processing Step
greedy algorithm B A A AB B
Graph connectivity
Geometry connectivity

11. Cost Assignment Schemes
The cost is assigned based on
BFS on each region of module.
Compromise BFS: involves adding
vertices & edges to the flow graph.
Details in paper.
Improved BFS: combination of
BFS & CBFS. 2 1 1 1 2 1 2

12. Comparison of Cost Schemes
The initial input (center position) is obtained from previous SA result (ami33 & ami49).
Size of constraining rectangle ranges from 1.96 to 3.24 times of modules’ required area.
Using C++ & LEDA and the running time is about 5 secs.

13. Sample output: ami49

14. Future Work
A more systematic post processing step to obtain a practical result.
How to convert a infeasible input into a feasible one.