A New Approach to the Rectilinear Steiner Tree Problem

We discuss a new approach to constructing the rectilinear Steiner tree (RST) of a given set of points in the plane, starting from a minimum spanning tree (MST). The main idea in our approach is to determine L-shaped layouts for the edges of the MST, so as to maximize the overlaps between the layouts, thus minimizing the cost (i.e., wire length) of the resulting RST. We describe a linear time algorithm for constructing a RST from a a MST, such that the RST is optimal under the restriction that the layout of each edge of the MST is an L-shape. The RST´s produced by this algorithm have 8-33% lower cost than the MST, with the average cost improvement, over a large number of random point sets, being about 9%. The running time of the algorithm on an IBM 3090 processor is under 0.01 seconds for point sets with cardinality 10. We also discuss a property of RST´s called stability under rerouting, and show how to stabilize the RST´s derived from our approach. Stability is a desirable property in VLSI global routing applications.