An O(bn/sup 2/) time algorithm for optimal buffer insertion with b buffer types

Buffer insertion is a popular technique to reduce the interconnect delay. The classic buffer insertion algorithm of van Ginneken has a time complexity of O(n/sup 2/), where n is the number of buffer positions. Lillis, Cheng, and Lin extended van Ginneken's algorithm to allow b buffer types in O(b/sup 2/n/sup 2/) time. For modern design libraries that contain hundreds of buffers, it is a serious challenge to balance the speed and performance of the buffer insertion algorithm. In this paper, we present a new algorithm that computes the optimal buffer insertion in O(bn/sup 2/) time. The reduction is achieved by the observation that the (Q,C) pairs of the candidates that generate the new candidates must form a convex hull. On industrial test cases, the new algorithm is faster than the previous best buffer insertion algorithms by orders of magnitude. Since van Ginneken's algorithm with multiple buffer types are used by most existing algorithms on buffer insertion and buffer sizing, our new algorithm improves the performance of all these algorithms.