Efficient buffer insertion algorithm for large networks based on Lagrangian relaxation

We propose a novel buffer insertion algorithm for handling more general networks, whose underlying topology is a directed acyclic graph rather than just a RC tree. The algorithm finds a global buffering which minimizes buffer area while meeting the timing constraints. We use Lagrangian relaxation to translate the timing constraints to a cost in the objective function, and simplify the resulting objective function using the special structure of the problem we are solving. The core of the algorithm is a local refinement procedure, which iteratively computes the optimal buffering for each edge so as to minimize a weighted area and delay objective. The resulting procedure is fast, and takes full advantage of the slack available on noncritical paths.