Steiner tree construction based on congestion for the global routing problem

Global routing is an essential part of physical design, and has been traditionally formulated to minimize either an estimate of the total wirelength or the channel capacity of a circuit ignoring important issues such as congestion and number of bends. In this paper, a mathematical programming model that combines the wirelength minimization model and the channel capacity minimization model is presented. The combined model is also capable of incorporating different aspects of the global routing problem, such as via-count and congestion in two stages of the global routing problem: route construction and problem formulation. In addition, numerical enhancements have been proposed to increase the speed of the global routing formulation. Experiments on different benchmarks show that the new model builds a flexible and powerful technique that enhances the global routing solution compared to other mathematical programming techniques developed for global routing.