# Provably Good Performance-Driven Global Routing

## Abstract

We 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. We first present several heuristics with good performance, based on an analog of Prim's minimum spanning tree construction. Next, we 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. This method is based on the following two results. First, for any given value of a parameter є, we can construct a routing tree with longest interconnection path length at most (1 + є) • R, and with cost at most (1 + (2/є)) times the minimum spanning tree weight. Moreover, for Steiner global routing in arbitrary weighted graphs, we achieve longest path length at most (1 + є). R, with wiring cost within a factor 2 • (1 + (2 /є)) of the optimal Steiner tree cost. In both cases, R is the minimum possible length from the source to the furthest sink. We also show that geometry helps in routing: in the Manhattan plane, the total wire length for Steiner routing improves to 3/2 • (1 + (1 /є)) times the optimal Steiner tree cost, while in the Euclidean plane, the total cost is further reduced to [formula Omitted] • (1 + (1/є)) times optimal. Furthermore, our 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, using a large set of examples which reflect both cell-based and building-block layout styles. © 1992 IEEE