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An exact model for multi-layer constrained via minimization

In this paper we consider the multi-layer con- strained via minimization problem which arises in the design of integrated circuits and printed circuit boards. That problem has been shown to be NP-complete even for two layers when the maximum junction degree is ≥ 4. We show that, for any maximum junction degree, for a given k, k ≥ 2, the problem can be reduced to the k-partite induced subgraph problem. We discuss integer programming formulations for that problem when k = 2 and k ≥ 3. Using this, we describe cutting plane algorithms for both cases, and present some experimental results. We also discuss some practical considerations such as the overlap case and show how these can be taken into account by our model.