High performance over-the-cell routing

Recently, several algorithms have been presented which use over-the-cell routing to minimize channel height in standard cell designs. A major shortcoming of the existing routers is the increase in the maximum wire length which may violate the timing constraints. In this paper, we consider the center terminal model, and the terminal assignment phase for over-the-cell routing so that the timing overhead of the routing meets a certain bound. We guarantee efficient terminal assignment by minimizing the maximum net span, a lower bound for the timing overhead, formally defined as the maximum Manhattan distance, among all nets, between the source and furthest destination on the net. We present an O(t²·logt) optimal dynamic programming algorithm for the maximum net span, and an efficient heuristic that couples net span and density minimization so that we obtain high performance routing with small channel width. Experimental results support the theoretical foundations of our approach