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

5.2 Predictive Pruning
During the van Ginneken’s algorithm, a candidate is pruned out only if there is another candidate
that is superior in terms of capacitance and slack. This pruning is based on the information at
the current node being processed. However, all candidates at this node must be propagated further
upstream toward the source. This means the load seen at this node must be driven by some minimal
amount of upstream wire or gate resistance. By anticipating the upstream resistance ahead of time,
one can prune out more potentially inferior candidates earlier rather than later, which reduces the
total number of candidates generated. More specifically, assume that each candidate must be driven
by an upstream resistance of at least R min . The pruning based on anticipated upstream resistance
is called predictive pruning.
Definition 1 (Predictive pruning) Let α 1 and α 2 be two nonredundant candidates of T(v) such
that C(α 1 ) < C(α 2 ) and Q(α 1 ) < Q(α 2 ). If Q(α 2 ) − R min · C(α 2 ) ≤ Q(α 1 ) − R min · C(α 1 ),
then α 2 is pruned.
Predictive pruning preserves optimality. The general situation is shown in Fig. 14. Let α 1 and
α 2 be candidates of T(v 1 ) that satisfy the condition in Definition 1. Using α 1 instead of α 2 will
not increase delay from v to sinks in v 2 ,...,v k . It is easy to see C(v,α 1 ) < C(v,α 2 ). If Q at v is
determined by T(v 1 ), we have
Q(v,α 1 ) − Q(v,α 2 ) = Q(v 1 ,α 1 ) − Q(v 1 ,α 2 ) − R min · (C(v 1 ,α 1 ) − C(v 1 ,α 2 ))
≥ 0
Therefore, α 2 is redundant.
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