Fiduccia–Mattheyses algorithm
A classical approach to solve the Hypergraph bipartitioning problem is an iterative heuristic by Charles Fiduccia and Robert Mattheyses. This heuristic is commonly called the FM algorithm.
Introduction
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, where P is the total # of terminals.
F–M heuristic: notation
Input: A hypergraph with a vertex set and a hyperedge set- n: # of cells in Net i; e.g., n = 4
- s: size of Cell i
- p: # of pins of Cell i; e.g., p = 4
- C: total # of cells; e.g., C = 13
- N: total # of nets; e.g., N = 4
- P: total # of pins; P = p + … + p = n + … + n
- Area ratio r, 0< r<1
- Cutsetsize is minimized
- |A|/ ≈ r