The mapping from a global routing to a feasible detailed routing in a number of 2D array routing structures has been shown to be an NP-complete problem. These routing structures include the Xilinx style routing architecture, as well as architectures with significantly higher switching flexibility. In response to this complexity, a different class of FPGA routing structures called Greedy Routing Architectures (GRAs) have been proposed. On GRAs, optimally routing each switch box, in a specified order, leads to an optimal chip routing. Because routing each switch box takes polynomial time, the mapping problem on GRAs can be solved in polynomial time. In particular, an H-tree GRA with W2+2W switches per switch box (SpSB) and a 2D array GRA with 4W2+2W SpSB have been proposed. In this paper, we improve on these results by introducing an H-tree GRA with W2/2+2W SpSB and a 2D array GRA with 3.5W2+2W SpSB. These new GRAs have the same desirable mapping properties of the previously described GRAs, but use fewer switches.

In this paper, we propose a hybrid hierarchical global router for multi-layer VLSI's, which executes routing and layering simultaneously. This novel approach, a hybrid hierarchical global router, is a combination of a topdown and a bottomup hierarchical routers, and may be one of interesting routing techniques. We also show experimental results, which demonstrate the superiority of the hybrid hierarchical approach. This approach may have many possibilities to be used in a various fields.