The efficient solution of integer programs for hierarchical global routing

Hierarchical methods for global routing are addressed. These methods break down the integer program that formulates the routing problem into small integer programs. These programs are solved exactly by using integer programming methods. Then the exact solutions of the small integer programs are pieced together to form an approximate solution of the original routing problem. The structure of the small integer programs is investigated. A greedy preprocessing method is proposed that, in effect, preroutes easily routable nets and reduces the remaining integer program to a fraction of the size in some cases, and eliminates it altogether in other cases. This yields a substantial reduction of the time required to solve the small integer programs