A Mixed HVH-VHV Algorithm for Three-Layer Channel Routing

We present a hybrid three-layer channel-routing algorithm that combines horizontal-vertical-horizontal (HVH) and vertical-horizontal-vertical (VHV) approaches [1]. The result is the best of both approaches. VHV excels when the vertical constraint graph (VCG) has long chains; HVH is strong when the VCG has a large number of incomparable nodes. In hybrid routing, the VCG is partitioned into two portions, one ideally suited for HVH and the other for VHV. The portions are routed with a transition track in between. It is shown that, for many channel-routing problems, the hybrid method can do with fewer tracks than the theoretical lower bounds of the algorithms given in [1][2][3]. A heuristic algorithm is given for determining an optimum partitioning into HVH and VHV portions. The algorithm is powerful and its performance on Deutsch's difficult example [8] is discussed as an illustration.