Single-Row Routing with Crossover Bound

Previous studies of the single-row routing problem have been restricted to the minimization of the total number of horizontal tracks needed for the realization of a given set of nets. Therefore, it has been assumed that enough space exists between adjacent nodes to allow for the wiring. Due to this assumption, realizations obtained with previously proposed algorithms may require a large number of vertical tracks between adjacent nodes. In this paper, we study the single-row routing problem when the number of vertical tracks available between adjacent nodes is bounded by a positive integer called the crossover bound. We give some results concerning crossovers and prove that, for any given positive integer K, an instance can be constructed such that the vertical track requirement between adjacent nodes cannot be less than K. We develop a fast algorithm for the case when the number of horizontal tracks available as well as the number of vertical tracks available between adjacent nodes have been preset. We compare the performance of our algorithm to the performance of an algorithm (proposed in [6]) which is fast and does not consider the vertical track constraint. Our experiments show that, in all cases, the realizations found by our algorithm have the same street capacities as those obtained by the algorithm proposed in [6]. However, unlike the realizations found with the algorithm proposed in [6], the ones found by our algorithm have smaller crossover bounds. The computing time of our algorithm is, in general, no worse than the computing time of the algorithm proposed in [6].