1. Min-Cut Placement

2. Algorithm

3. Min-Cut Placement for Standard Cells
Quadrature:
Suitable for netlists with high density in the center
Bisection:
For general standard cell placement (may result in greater wirelength)
Slice/bisection:
Suitable for netlists with high interconnections on the periphery

4. Min-Cut Placement – Example
Details in the text book
Given:
cut1 1 4 2 5 6 3
Task: 4 x 2 placement with minimum wirelength using alternative cutline directions and the KL algorithm

5. Min-Cut Algorithm: Example1 4 2 5 6 3
Vertical cut cut1: L={1,2,3}, R={4,5,6} 1 4 1 4 5 2 5 2 3 6 3 6
KL Algorithm
cut1
cut1

6. 1 4 5 2 3 6
cut1
Horizontal cut cut2L: T={1,4}, B={2,0}
Horizontal cut cut2R: T={3,5}, B={6,0} 1 4 3 5
cut2L
cut2R 2 6 1 2 4 5 3 6
cut3BL
cut3BR
cut3TL
cut3TR 1 4 5 3 2 6

7. Min-Cut for Macrocell Placement1 2 3

8. Min-Cut for Macrocell Placement
Partitioning of 412-cell circuit into groups of size <= 6

9. Terminal Propagation TR 2 3 2 2 3 4 3 1 1 4 1 4 BR
Terminal Propagation
External connections are represented by artificial connection points on the cutline
Dummy nodes in hypergraphs 2 1 4 3 x 2 1 4 3 p‘ BR TR 1 2 4 3
© 2011 Springer Verlag

10. Terminal Propagation Example

11. Terminal Propagation (Order Dependence)

12. Min-Cut Placement Reasonably fast
Advantages:
Reasonably fast
Objective function can be adjusted, e.g., to perform timing-driven placement
Hierarchical strategy applicable to large circuits
Disadvantages:
Randomized, chaotic algorithms – small changes in input lead to large changes in output
Optimizing one cutline at a time may result in routing congestion elsewhere