Routability crossing distribution and floating terminal assignment of T-type junction region

In this paper, two routability crossing distribution problems based on the non-crossing relations, vertical constraint relations and geometry relations are proposed to improve routing performance of one T-type junction region. For the routability problem, a routability ordering graph can be built to decide a net ordering on the boundary in O(n²) time. Furthermore, for the routability quota problem, if the number of crossings for the routability problem is more than the quota, the net ordering in the routability problem must be adjusted by a net interchange operation to satisfy the quota requirement in the routability quota problem in O(n) time. Since a net ordering is obtained in the routability problem or the routability quota problem, the global nets will be assigned onto the boundary in O(n) time by interleaving vacant terminals between any pair of global nets for the floating terminal assignment of the boundary