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

3.2.2 Buffer insertion
Suppose that we add a buffer b at u. γ u is then updated to γ ′ u where
Q(γ ′ u) = Q(γ u ) − (R(b) · C(γ u ) + K(b)),
C(γ ′ u) = C(b).
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3.2.3 Branch merging
When two branches T l and T r meet at a branching point v, Γ l and Γ r , which correspond to T l and
T r , respectively, are to be merged. The merging process is performed as follows. For each solution
γ l ∈ Γ l and each solution γ r ∈ Γ r , generate a new solution γ ′ according to:
C(γ ′ ) = C(γ l ) + C(γ r ),
Q(γ ′ ) = min{Q(γ l ),Q(γ r )}.
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The smaller Q is picked since the worst-case circuit performance needs to be considered.
3.3 Inferiority and Pruning Identification
Simply propagating all solutions by the above three operations makes the solution set grow exponentially
in the number of buffer positions processed. An effective and efficient pruning technique
is necessary to reduce the size of the solution set. This motivates an important concept - inferior
solution - in van Ginneken’s algorithm. For any two partial solutions γ 1 ,γ 2 at the same vertex v, γ 2
is inferior to γ 1 if C(γ 1 ) ≤ C(γ 2 ) and Q(γ 1 ) ≥ Q(γ 2 ). Whenever a solution becomes inferior, it is
pruned from the solution set. Therefore, only solutions excel in at least one aspect of downstream
capacitance and slack can survive.
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