Two new efficient approximation algorithms with O(k log k) for the Steiner tree problem in rectilinear graphs

The authors propose two new approximation algorithms with a time complexity of O(k log k) (k is the number of the given generating points) for the rectilinear Steiner tree problem. Both algorithms make use of the modified Delaunay net defined by the given generating points and the derived triangular Steiner points. In order to make successively a minimum spanning subtree on the modified Delaunay net, the authors use doubly the neighborhood property of each triangular Steiner point as well as each generating point for the first method, and use Kruskal's algorithm-like procedure for the second method