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

3 Van Ginneken’s algorithm
For a general case of signal nets, which may have multiple sinks, van Ginneken’s algorithm [11]
is perhaps the first systematic approach on buffer insertion. For a fixed signal routing tree and
given candidate buffer locations, van Ginneken’s algorithm can find the optimal buffering solution
that maximizes timing slack according to the Elmore delay model. If there are n candidate buffer
locations, its computation complexity is O(n 2 ). Based on van Ginneken’s algorithm, numerous
extensions have been made, such as handling of multiple buffer types, tradeoff with power and
cost, addressing slew rate and crosstalk noise, using accurate delay models and speedup techniques.
These extensions will be covered in subsequent sections.
At a high level, van Ginneken’s algorithm [11] proceeds bottom-up from the leaf nodes toward
the driver along a given routing tree. A set of candidate solutions keep updated during the process,
where three operations adding wire, inserting buffers and branch merging may be performed.
Meanwhile, the inferior solutions are pruned to accelerate the algorithm. After a set of candidate
solutions are propagated to the source, the solution with the maximum required arrival time is
selected as the final solution. For a routing tree with n buffer positions, the algorithm computes
the optimal buffering solution in O(n 2 ) time.
A net is given as a binary routing tree T = (V,E), where V = {s 0 }∪V s ∪V n , and E ⊆ V ×V .
Vertex s 0 is the source vertex and also the root of T , V s is the set of sink vertices, and V n is the
set of internal vertices. In the existing literatures, s 0 is also referred as driver. Denote by T(v)
the subtree of T rooted at v. Each sink vertex s ∈ V s is associated with a sink capacitance C(s)
and a required arrival time (RAT). Each edge e ∈ E is associated with lumped resistance R(e)
and capacitance C(e). A buffer library B containing all the possible buffer types which can be
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