An exact algorithm for single-layer wire-length minimization

Consider a given single-layer detailed routing L of a set of two-terminal nets. The authors present necessary and sufficient conditions for a layout to have minimum length under homotopic transformations (i.e., without changing the given global routing). Based on the proposed classification and the notion of line-segment visibility, the authors present an exact algorithm that minimizes the total wire-length of L. The proposed algorithm runs in O(n/sup 2/) time, where n is the number of bends in L. For the class of x-monotone layouts (i.e., each vertical line crosses each wire once at most) an O(n log n) time algorithm is proposed.<>