Over-the-Cell Channel Routing1

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, (3) routing within the channel. In this paper, we show that the first step can be reduced to the problem of finding a maximum independent set of a circle graph, and thus, can be solved optimally in quadratic time. Also, we show that to determine an optimal choice of net segments in the second step is NP-hard in general, and we present an efficient heuristic algorithm for this step. The third step can be carried out using a conventional channel router. Based on these theoretical results, we design an over-the-cell channel router that produces solutions which are better than the optimal two-layer channel routing solutions for all test examples. Our over-the-cell channel router also outperforms the over-the-cell channel router in [19]. In particular, for the famous Deutsch’s Difficult Example, our 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 in [19].