1. A Linear-Time Heuristic for Improving Network Partitions
C. M. Fiduccia
R. M. Mattheyses

2. Calculating Gain g(i) = FS(i) - TE(i) FS(i) TE(i)
The number of nets which only contain cell i and not connected to any other cell in the same partition as cell i
TE(i)
The number of nets that connect to cell i and only other cells currently in the same partition as cell i

3. Example Gain
cell FS TE
gain 1 2 +2 +1 3 4 -1

4. Example Gain

5. Calculate Gain For each free cell i do G(I) = 0
F = the “from block” of cell(i)
T = the “to block” of cell(i)
For each net n on cell i do
If F(n) = 1 increment g(i)
If F(n) = 0 increment g(i)
End for

6. Balance Condition
Where r is the tolerance factor (usually close to 0.5)
V is the full set of cells
A is the set of cells in partition A
smax is the maximum cell size

7. Fiduccia-Mattheyses
Select the cell with the greatest gains that satisfies balance conditions
Swap the cell and lock it
Update gains
Repeat until all cells are locked or will dissatisfy balance conditions

8. Fiduccia-Mattheyses Create an initial partition
Iteratively execute the FM heuristic
Start again using the result partition as the initial partition
Continue until the resulting gain is no longer greater than zero

9. Results Total Cells Total Nets gain Avg gain 50 100 25 23 28 25.3 500
1000
211
233
215
219.6
2500
422
429
414
421.6