A Multilevel Congestion-Based Global Router

Routing in nanometer nodes creates an elevated level of importance for low-congestion routing. At the same time, advances in mathematical programming have increased the power to solve complex problems, such as the routing problem. Hence, new routing methods need to be developed that can combine advanced mathematical programming and modeling techniques to provide low-congestion solutions. In this paper, a hierarchical mathematical programming-based global routing technique that considers congestion is proposed. The main contributions presented in this paper include (i) implementation of congestion estimation based on actual routing solutions versus purely probabilistic techniques, (ii) development of a congestion-based hierarchy for solving the global routing problem, and (iii) generation of a robust framework for solving the routing problem using mathematical programming techniques. Experimental results illustrate that the proposed global router is capable of reducing congestion and overflow by as much as 36% compared to the state-of-the-art mathematical programming models