New algorithms for 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 find 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 rectilinear Steiner tree. We describe two algorithms for constructing rectilinear Steiner trees from MST’s, that are optimal under the conditions that the layout of each edge of the MST is (1) a L-shape, or (2) any staircase, respectively. The first algorithm has linear time complexity and the second algorithm has a higher polynomial time complexity. Steiner trees produced by the second algorithm have a property called stability, which enables the rerouting of any segment of the tree, while maintaining the cost of the tree, and not causing overlaps with the rest of the tree. Stability is a desirable property in VLSI global routing applications.