Over-the-cell channel routing

A common approach to the over-the-cell channel routing problem is to divide the problem into three steps: (1) routing over the cells; (2) choosing net segments; and (3) routing within the channel. It is shown that the first step can be reduced to the problem and finding a maximum independent set of a circle graph, and thus can be solved optimally in quadratic time. Also, it is shown that to determine an optimal choice of net segments in the second step is NP-hard in general, and an efficient heuristic algorithm for this step is presented. The third step can be carried out using a conventional channel router. On the basis of these theoretical results, an over-the-cell channel router that produces solutions which are better than the optimal two-layer channel routing solutions for all test examples is designed. The over-the-cell channel router also outperforms the over-the-cell channel router described by Y. Shiraishi and Y. Sakemi (ibid., vol.CAD-6, no.3, p.462-71, 1987). In particular, for Deutsch´s difficult example, the solution yields a saving of 10.5% in channel routing area when compared with the optimal two-layer channel routing solution, and a saving of 15% in channel routing area when compared with the routing solution produced by the over-the-cell channel router