$O(mn)$ Time Algorithm for Optimal Buffer Insertion of Nets With $m$ Sinks

Buffer insertion is an effective technique to reduce interconnect delay. In this paper, we give a simple
$O(mn)$
time algorithm for optimal buffer insertion, where
$m$
is the number of sinks and
$n$
is the number of buffer positions. When
$m$
is small, our algorithm is a significant improvement over the recent
$O(n\log^{2}n)$
time algorithm by Shi and Li, and the
$O(n^{2})$
time algorithm of van Ginneken. For
$b$
buffer types, our algorithms runs in
$O(b^{2}n+bmn)$
time, an improvement of the recent
$O(bn^{2})$
algorithm by Li and Shi. The improvement is made possible by an innovative linked list that can perform addition of a wire, addition of a buffer in amortized
$O(1)$
time, and smart design of pointers. We then present the extension of our algorithm for the buffer cost minimization problem, which improves the previous best algorithm. On industrial test cases, the new algorithms is faster than previous best algorithms by an order of magnitude.