Rectilinear Steiner tree construction by local and global refinement

Presents a new algorithm for constructing a rectilinear Steiner tree (RST) for a given set of points. Starting from a rectilinear minimum spanning tree (MST), the algorithm works by incrementally introducing “good” Steiner points into the point set and generating an MST from the enlarged point set. Steiner points are introduced in two stages according to their essentiality and cost. In the first stage, they are generated from the local structure of the tree; in the second stage, they are generated from the global structure using a loop detection method. The proposed algorithm outperforms most other algorithms of its class by the fact that the average cost improvement over the rectilinear minimum spanning tree is 10.4%, and its time complexity is O(n² log n)