On Routing for Custom Integrated Circuits

This paper presents a novel and effective strategy for routing custom integrated circuits as well as solutions to subproblems associated with this strategy. Given an initial placement of rectangular blocks, the routing strategy includes the following major steps: construction of a channel graph, estimation of channel widths (based on a statistical model for signal nets and topological routing of power and ground nets), placement modification to include the estimated channel widths, topological routing for signal nets, and finally track assignment. Besides presenting an overview of our strategy, the following topics will be discussed in some detail: (1) necessary and sufficient conditions and a simple algorithm for single layer topological routing of power and ground nets, (2) a quadratic programming formulation for the placement modification problem, and (3) a fast algorithm for obtaining topological routes for signal nets.