Provably good performance-driven global routing

The authors propose a provably good performance-driven global routing algorithm for both cell-based and building-block design. The approach is based on a new bounded-radius minimum routing tree formulation. The authors first present several heuristics with good performance, based on an analog of Prim´s minimum spanning tree construction. Next, they give an algorithm which simultaneously minimizes both routing cost and the longest interconnection path, so that both are bounded by small constant factors away from optimal. They also show that geometry helps in routing: in the Manhattan plane, the total wire length for Steiner routing improves to 3/2×(1+(1/ε)) times the optimal Steiner tree cost, while in the Euclidean plane, the total cost is further reduced to (2/√3)×(1+(1/ε)) times optimal. The method generalizes to the case where varying wire length bounds are prescribed for different source-sink paths. Extensive simulations confirm that this approach works well