A provably good algorithm for high performance bus routing

As the clock frequencies used in industrial applications increase, the timing requirements on routing problems become tighter, and current routing tools can not successfully handle these constraints any more. We focus on the high-performance single-layer bus routing problem, where the objective is to match the lengths of all nets belonging to each bus. An effective approach to solve this problem is to allocate extra routing resources around short nets during routing; and use those resources for length extension afterwards. We first propose a provably optimal algorithm for routing nets with min-area max-length constraints. Then, we extend this algorithm to the case where minimum constraints are given as exact length bounds. We also prove that this algorithm is optimal within a constant factor. Both algorithms proposed are also shown to be scalable for large circuits, since the respective time complexities are O(A) and O(A log A), where A is the area of the intermediate region between chips.