The 60 degrees grid : routing channels in width d/ square root 3

Abstract

The 60 degrees grid consists of vertical columns and diagonal tracks running at slopes of +or-30 degrees . 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/ square root 3. The authors present two near-optimal channel routing algorithms. The first uses 5 layers and always routes in width at most d/ square root 3+ square root 3. The second algorithm uses at most 4 layers and routes in width omega , where d/ square root 3+O(1)>