1. Hagen-Kahng EIG Partitioning
Perform EIG partitioning and minimize ratio cut cost.
Clique-based graph model: dotted edge has weight of 0.5, and solid edge with no label has weight of 0.25.
Practical Problems in VLSI Physical Design

2. Adjacency Matrix
Practical Problems in VLSI Physical Design

3. Degree Matrix
Practical Problems in VLSI Physical Design

4. Laplacian Matrix We obtain Q = D − A
Practical Problems in VLSI Physical Design

5. Eigenvalue/vector Computation
Practical Problems in VLSI Physical Design

6. EIG Partitioning
Practical Problems in VLSI Physical Design

7. EIG Partitioning (cont)
Practical Problems in VLSI Physical Design

8. EIG Partitioning (cont)
Practical Problems in VLSI Physical Design

9. EIG Partitioning (cont)
Practical Problems in VLSI Physical Design

10. Summary Good solution found:
{(a,f,d,g,i), (j,b,h,e,c)} is well-balanced and has low RC cost.
Practical Problems in VLSI Physical Design

11. Theorem
Practical Problems in VLSI Physical Design