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As gate delays decrease faster than wire delays for each technology generation, buffer insertion becomes a popular method to reduce the interconnect delay. Several modern buffer insertion algorithms (e.g., [7, 6, 15]) are based on van Ginneken's dynamic programming paradigm [14]. However, van Ginneken's original algorithm does not control buffering resources and tends to over-buffering, thereby wasting area and power. It has been a major open problem whether it is possible to optimize slack and at the same time minimize the buffer usage.This paper settles this open problem by showing that for arbitrary integer cost functions, the problem is NP-complete. We also extend the pre-buffer slack technique [12] to minimize the buffer cost. This technique can significantly reduce the running time and memory in buffer cost minimization problem. The experimental results show that our algorithm can speed up the running time up to 17 times and reduces the memory to 1/30 of traditional best know algorithm. Finally, we show how to efficiently deal with multiway merge in buffer insertion.

Complexity analysis and speedup techniques for optimal buffer insertion with minimum cost