Multi-layer constrained via minimization with conjugate conflict continuation graphs

In this paper we present a new graph model, called a conjugate conflict continuation graph, especially to address the stacked via problem in multi-layer constrained via minimization (MCVM). An integer linear programming model (which is the first of its kind) and a simulated annealing (SA) algorithm are developed to solve MCVM. The SA algorithm on average achieves 6.4% via reduction for the layouts obtained by a commercial tool under a very restricted situation where the metal wires (including pins) used in cell layouts, power rails and rings, and clock routing are treated as obstacles or fixed objects to MCVM.