Optimal routing of two rectangular blocks

The problem in LSI/VLSI layout design of routing nets interconnecting two rectangular blocks is considered. Properties that determine horizontal-track (H-track) sharing between nets are identified. It is shown that H-track sharing can essentially be treated as pad-position-independent. For any case of colinearity constraints and interaction between nets in certain edge sets, the number of H-tracks required for routing is at most one more than for the case in which there are no such constraints. A share-graph model that models the H-track sharing between edge sets is developed. H-track sharing between nets in edge sets whose direction of routing is uniquely determined is first considered. Then nets that have alternate paths but use the same number of H-tracks are added to the north and south share-graphs. Algorithms to operate on these share-graphs to provide optimal H-track sharing are developed. The vertical track (V-track) sharing problem is considered as a matching problem in which a net routed to the south of the minimum enclosing rectangle must be matched to a net routed to the north