Constrained

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.

3
Proposed Design Flow
No
Bound-Feasible
Yes
No
Connected?
Yes
4
The Constrained Modern Floorplanning
Problem(CMFP)
Module Center W H Required Area
A (30,30) 60 60 2500
B (75,50) 50 100 4000
C (50,75) 100 50 3500

• 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 60 2500
B (75,50) 50 100 4000
C (50,75) 100 50 4500
6
Feasibility Analysis
(0,0)
Center Area W H
A (50,50) 8000 100 100
B (135,55) 12000 130 110
C (235,45) 10000 130 90
D (75,145) 12000 150 110
E (220,125) 18000 160 150
(300,200)
7
Region Identification
3
C
A
B
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)
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
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.

1
2
1
0
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.