The 60° grid : routing channels in width d/√3

The 60° grid consists of vertical columns and diagonal tracks running at slopes of ±30°. This model offers a potentially large reduction in channel width, without resorting to wire overlap. For a channel routing problem with density d, the availability of the diagonal tracks leads to a lower bound of d/√3. The authors present two near-optimal channel routing algorithms. The first uses 5 layers and always routes in width at most d/√3+√3. The second algorithm uses at most 4 layers and routes in width ω, where d/√3+O(1)⩽ω⩽d/√3+O(√d)