Circuit Partitioning

1
Circuit Partitioning

• Divides circuit into smaller partitions that can
  be efficiently handled
• Goal is generally to minimize communication
  between balanced partitions
• Kernighan-Lin Fiduccia-Mattheyses (KLFM) is
  popular algorithm

2
KLFM Algorithm

• Basic Idea
• Start with initial partition
• Iteratively improves cutsize
• Cutsize is number of edges between partitions
• Moves one node at a time
• Node that gives greatest reduction or least
  degradation
• Lock node after moving
• Continue moving nodes until all locked or size
  contraints are violated
• Find best partitioning, unlock all nodes
• Repeat until no improvement found

3
KLFM Algorithm
Initial Partition
Maximum Size 4
Size 3
Size 3
Cutsize 5
4
KLFM Algorithm
Maximum Size 4
Size 4
Size 2
Cutsize 3
5
KLFM Algorithm
Maximum Size 4
Size 3
Size 3
Cutsize 2
6
KLFM Algorithm
Maximum Size 4
Size 2
Size 4
Cutsize 2
7
KLFM Algorithm
Maximum Size 4
Size 3
Size 3
Cutsize 4
8
KLFM Algorithm
Maximum Size 4
Size 2
Size 4
Cutsize 4
9
KLFM Algorithm
Maximum Size 4
Size 3
Size 3
Cutsize 5
10
KLFM Algorithm
Backtrack to minimum cut size, unlock nodes, and
repeat
Size 3
Size 3
Cutsize 2