Channel density reduction by routing over the cells

We propose a new approach for reducing the density of a channel by routing some nets (or subnets) over the cells (i.e., outside the channel). Previous research assumed that the more nets being routed over the cells the greater the reduction in the channel density. We show that only the removal of critical nets contributes to the re- duction in the channel density. We divide channel into zones where each zone has a zone density and the removal of any net from a zone will reduce its density by one. In order to reduce the channel density, only certain critical zones need to have their nets routed over the cells. A bipartite graph is used to represent the relationship between nets and zones. The problem is transformed into a constrained covering problem and formulated as an integer linear programming problem. In comparison with previous research, our approach reduces more channel densities while using fewer tracks over the cells. For Deutsch's difficult khannel, a previous aiiproach needs 15 tracks over the cells to reduce the channel density by 3 while we need only 5 tracks to achieve the same result . Index Terms-Over-the-cell routing, channel density reduction, stan- dard-cell layout, VLSI routing, integer linear programming.