Solving the net matching problem in high-performance chip design

In high-performance chip design, the problem of net matching is often critical for achieving correct circuit performance. We adopt a conservative design, to route all matched nets with identical topologies and equal wire lengths to achieve zero skew. The problem is formulated as a variant of the D-dimensional Steiner tree problem. We propose a two-stage solution. The first stage uses an iterative improvement strategy to generate the Steiner tree topology for all the nets. The second stage places the nodes using one of two methods. The first approach expresses the optimal Steiner node positions as a linear programming solution, with average computational complexity O(n² m²), where n is the number of nets and m is the number of pins. Improved efficiency is achieved under the other approach by transforming the Manhattan metric to an l_∞ norm using a 45° rotation of the solution space. The norm is then approximated by either an l_λ norm, for suitably large values of λ, or an exponential “penalty” function. The solution space in both approaches becomes strictly convex, allowing us to apply a greedy approach which converges to an optimal solution with great efficiency, leading to a dramatic speed-up versus the linear programming approach