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

the algorithm maintains two solution sets, one for positive and one for negative buffer input polarity.
After choosing the best solution at driver, the buffer assignment can be then determined by a
top-down traversal. The details of the new algorithm are elaborated as follows.
Denote the two solution sets at vertex v by Γ + v and Γ − v corresponding to positive polarity and
negative polarity, respectively. Supposed that an inverter b − is inserted to a solution γ v + ∈ Γ + v ,
a new solution γ v ′ is generated in the same way as before except that it will be placed into Γ − v .
Similarly, the new solution generated by inserting b − to a solution γv − ∈ Γ − v will be placed into Γ + v .
For inserting a non-inverting buffer, the new solution is placed in the same set as its origin.
The other operations are easier to handle. The wire insertion goes the same as before and two
solution sets are handled separately. Merging is carried out only among the solutions with the same
polarity, e.g., the positive-polarity solution set of left branch is merged with that of the right branch.
For inferiority check and solution pruning, only the solutions in the same set can be compared.
4.4 Slew and Capacitance Constraints
The slew rate of a signal refers to the rising or falling time of a signal switching. Sometimes
the slew rate is referred as signal transition time. The slew rate of almost every signal has to be
sufficiently small since a large slew rate implies large delay, large short circuit power dissipation
and large vunlerability to crosstalk noise. In practice, a maximal slew rate constraint is required
at the input of each gate/buffer. Therefore, this constraint needs to be obeyed in a buffering algorithm
[12–15].
A simple slew model is essentially equivalent to the Elmore model for delay. It can be explained
using a generic example which is a path p from node v i (upstream) to v j (downstream) in a buffered
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