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

assigned to a buffer position is also given. In this section, B contains only one buffer type. Delay
estimation is obtained using the Elmore delay model, which is described in Chapter 3. A buffer
assignment γ is a mapping γ : V n → B ∪{b} where b denotes that no buffer is inserted. The timing
buffering problem is defined as follows.
Timing Driven Buffer Insertion Problem: Given a binary routing tree T = (V,E), possible buffer
positions, and a buffer library B, compute a buffer assignment γ such that the RAT at driver is
maximized.
3.1 Concept of Candidate Solution
A buffer assignment γ is also called a candidate solution for the timing buffering problem. A
partial solution, denoted by γ v , refers to an incomplete solution where the buffer assignment in
T(v) has been determined.
The Elmore delay from v to any sink s in T(v) under γ v is computed by
D(s,γ v ) =
∑
(D(v i ) + D(e)),
e=(v i ,v j )
where the sum is taken over all edges along the path from v to s. The slack of vertex v under γ v is
defined as
Q(γ v ) = min {RAT(s) − D(s,γ v )}.
s∈T(v)
At any vertex v, the effect of a partial solution γ v to its upstream part is characterized by a
(Q(γ v ),C(γ v )) pair, where Q is the slack at v under γ v and C is the downstream capacitance
viewing at v under γ v .
7