Congestion based mathematical programming models for global routing

Global routing is an essential part of physical design, and has been traditionally formulated to minimize either the total wirelength or the maximum channel capacity of a circuit ignoring important issues such as congestion and number of bends. In this paper, a mathematical programming model, which is capable of incorporating different aspects of the global routing problem, such as wirelength, maximum capacity, number of bends in each route and congestion is presented. The main advantage of this model is its flexibility to deal with different aspects of the routing. Our congestion estimation gives lower and upper estimates on the maximum number of wires passing through each channel. Experiments on different benchmarks show that the new model builds a flexible and powerful technique which enhances the global routing solution.