A classical approach to solve the Hypergraph bipartitioning problem is an iterative heuristic by Fiduccia and Mattheyses. This heuristic is commonly called the FM algorithm.
FM algorithm is a linear time heuristic for improving network partitions. New features to K-L heuristic:
Aims at reducing net-cut costs; the concept of cutsize is extended to hypergraphs.
Only a single vertex is moved across the cut in a single move.
Vertices are weighted.
Can handle "unbalanced" partitions; a balance factor is introduced.
A special data structure is used to select vertices to be moved across the cut to improve running time.
Time complexity O(P), where P is the total # of terminals.
Input: A hypergraph with a vertex (cell) set and a hyperedge (net) set
n(i): # of cells in Net i; e.g., n(1) = 4
s(i): size of Cell i
p(i): # of pins of Cell i; e.g., p(1) = 4
C: total # of cells; e.g., C = 13
N: total # of nets; e.g., N= 4
P: total # of pins; P= p(1) + … + p(C) = n(1) + … + n(N)
Area ratio r, 0< r<1
Output: 2 partitions
Cutsetsize is minimized
|A|/(|A|+|B|) ≈ r
