Diagonal channel routing with vias at unit distance

We consider the «diagonal» channel routing model (DM), where the connections are laid in two layers, along tracks at +45° and ?45° respectively. A previous result [10] shows that, for a channel routing problem of density d, a DM layout exists with channel width w=2d. However, vias may appear at a distance 1/tr2. We prove here that another DM layout can be constructed with w-kd, k constant, and all vias at a distance ≥1. By a theoretical point of view this layout is superior to the one obtained in the classical Manhattan Model, in the worst case.