On the Crossing Distribution Problem in Two Regions

VLSI layout design is typically decomposed into four steps: placement, global routing, routing region definition and ordering, and detailed routing. The crossing distribution problem occurs prior to detailed routing, in which crossings of nets are distributed according to design constraints. In this paper, we propose an O(nlog n) time algorithm for the crossing distribution problem for two-terminal nets in two regions, where n is the number of nets. This algorithm improves a previously known result that runs in O(n2) time [6]. We also give an O(n2) time algorithm for the crossing distribution problem for three-terminal nets under some assumption