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

and those dictated by solutions in Γ r are
(278, 59), (308, 74).
After pruning inferior solutions, the solution set at v 1 is
{(167, 19), (207, 39), (278, 59), (308, 74)}.
4 Van Ginneken Extensions
4.1 Handling Library with Multiple Buffers
We extend the standard van Ginneken’s algorithm to handle multiple buffers and buffer cost [12].
The buffer library B now contains various types of buffers. Each buffer b in the buffer library has
a cost W(b), which can be measured by area or any other metric, depending on the optimization
objective. A function f : V n → 2 B specifies the types of buffers allowed at each internal vertex in
T . The cost of a solution γ, denoted by W(γ), is defined as W(γ) = ∑ b∈γ W b. With the above
notations, our new problem can be formulated as follows.
Minimum Cost Timing Constrained Buffer Insertion Problem: Given a binary routing tree T =
(V,E), possible buffer positions defined using f, and a buffer library B, to compute a minimalcost
buffer assignment γ such that the RAT at driver is smaller than a timing constraint α.
In contrast to the single buffer type case, W is introduced into the (Q,C) pair to handle buffer
cost, i.e., each solution is now associated with a (Q,C,W)-triple. As such, during the process of
bottom-up computation, additional efforts need to be made in updating W : if γ ′ is generated by
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