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

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

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

Example Gain

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

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

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

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

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