Order of Channels for Safe Routing and Optimal Compaction of Routing Area

For a given placement of blocks and global routing of nets, a new formulation and its solution of the problem of determining the order of channels for the complete channel routing are presented. If the order of channels satisfying the condition exists, it is called the safe order since following it, each channel can be routed the wiring requirement without any prediction of necessary width. Thus the compaction of the routing area can be made utmost each time. The idea is based on the general feature of channel routers not on any particular one. Related subjects such as the simultaneously routable channels, generalization of the safe order, switch box routing, and the placement with nonrectangular blocks are discussed.