Buffer Insertion Basics - Computer Engineering & Systems Group ...

3.5 Example
Algorithm: van Ginneken’s algorithm.
Input: T : routing tree, B: buffer library
Output: γ which maximizes slack at driver
1. for each sink s, build a solution set {γ s }, where
Q(γ s ) = RAT(s) and C(γ s ) = C(s)
2. for each branching point/driver v t in the order given by
a postorder traversal of T , let T ′ be each of the branches T 1 ,
T 2 of v t and Γ ′ be the solution set corresponding to T ′ , do
3. for each wire e in T ′ , in a bottom-up order, do
4. for each γ ∈ Γ ′ , do
5. C(γ) = C(γ) + C(e)
6. Q(γ) = Q(γ) − D(e)
7. prune inferior solutions in Γ ′
8. if the current position allows buffer insertion, then
9. for each γ ∈ Γ ′ , generate a new solution γ ′
10. set C(γ ′ ) = C(b)
11. set Q(γ ′ ) = Q(γ) − R(b) · C(γ) − K(b)
12. Γ ′ = Γ ′ ⋃ {γ ′ } and prune inferior solutions
13. // merge Γ 1 and Γ 2 to Γ vt
14. set Γ vt = ∅
15. for each γ 1 ∈ Γ 1 and γ 2 ∈ Γ 2 , generate a new solution γ ′
16. set C(γ ′ ) = C(γ 1 ) + C(γ 2 )
17. set Q(γ ′ ) = min{Q(γ 1 ),Q(γ 2 )}
18. Γ vt = Γ vt
⋃ {γ ′ } and prune inferior solutions
19. return γ with the largest slack
Figure 4: Van Ginneken’s algorithm.
Let us look at a simple example to illustrate the work flow of van Ginneken’s algorithm. Refer to
Figure 5. Assume that there are three non-dominated solutions at v 3 whose (Q,C) pairs are
(200, 10), (300, 30), (500, 50),
and there are two non-dominated solutions at v 2 whose (Q,C) pairs are
(290, 5), (350, 20).
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