Congestion analysis for global routing via integer programming

This work presents a fast and flexible framework for congestion analysis at the global routing stage. It captures various factors that contribute to congestion in modern designs. The framework is a practical realization of a proposed parameterized integer programming formulation. The formulation minimizes overflow inside a set of regions covering the layout which is defined by an input resolution parameter. A resolution lower than the global routing grid-graph creates regions that are larger in size than the global-cells. The maximum resolution case simplifies the formulation to minimizing the total overflow which has been traditionally used as a metric to evaluate routability. A novel contribution of this work is to demonstrate that for a small analysis time budget, regional minimization of overflow with a lower resolution allows a more accurate identification of the routing congestion hotspot locations, compared to minimizing the total overflow. It allows generating a more accurate congestion heatmap. The other contributions include several new ideas for a practical realization of the formulation for industry-sized benchmark instances some of which are also improvements to existing global routing procedures. This work also describes coalesCgrip, a simpler variation of our framework which was used to evaluate the ISPD 2011 contest.