Non-uniform multilevel analog routing with matching constraints

Symmetry, topology-matching, and length-matching constraints are three major routing considerations to improve the performance of an analog circuit. Symmetry constraints are specified to route matched nets symmetrically with respect to some common axes. Topology-matching constraints are commonly imposed on critical yet asymmetry nets with the same number of bends, vias, and wirelength. Length-matching constraints are specified to route the nets which have limited resources with the same wirelength. These three constraints can reduce current mismatches and unwanted electrical effects between two critical nets. In this paper, we propose the first work to simultaneously consider the three constraints for analog routing while minimizing total wirelength, bend numbers, via counts, and coupling noise at the same time. We first present an integer linear programming (ILP) formulation to simultaneously consider the three constraints for analog routing, and employ effective reduction techniques to further reduce the numbers of ILP variables and constraints. Then, a non-uniform multilevel routing framework is presented to enhance the performance of our routing algorithm. Experimental results show that our approach can obtain better routing results and satisfy all specified routing constraints while optimizing circuit performance.