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, (3) routing within the channel. It is shown 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 O(n/sup 2/) time. It is also 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 done easily using a conventional channel router. Based on these theoretical results, an over-the-cell channel router was designed which produces better solutions than by the over-the-cell router of Y. Shiraishi and Y. Sakemi (IEEE Trans. Computer-Aided Design, vol.6, no.3, p.462-71, 1987).<>