Single phase three-layer channel routing algorithms

We present a simple three-layer assignment algorithm for planar layouts generated by a class of layout algorithms. This class of algorithms includes simple variations of the following algorithms developed by Mehlhorn et al. (1986): (i) The algorithm that generates planar layouts for the two-terminal net CRP with dmax tracks. (ii) The algorithm that generates planar layouts for the twoand three-terminal net CRP with at most L3dmax/2 J tracks. (iii) The algorithm that generates planar layouts for the multiterminal net CRP with at most 2dmax 1 tracks. The planar layouts generated by these algorithms are three-layer wirable by the layer assignment algorithm given in Preparata and Lipski (1984). Our approach is different. We make slight modifications to these layout algorithms and incorporate a simple layer assignment strategy to generate three-layer wirings. Our algorithms are faster and conceptually simpler because there is no need to construct diagonal diagrams and legal partitions. The channel width of the wiring generated by our algorithm is identical to that of the corresponding planar layout generated by algorithms (i)-(iii). Our layer assignment methodology can also be used to develop other single-phase three-layer algorithms, as demonstrated by Wieners-Lummer (1991).