A new heuristic for rectilinear Steiner trees

A heuristic algorithm for finding RSTs (rectilinear Steiner trees) is presented. The algorithm was run on a large number of randomly generated data sets. However, the algorithm performed exceptionally well for several data sets, namely, it found steiner trees whose total length was 15 to 18% less than the total length of the corresponding RMSTs (rectilinear minimum spanning trees). The time complexity of the heuristic is O(N log N). The heuristic algorithm is described, and an example is presented. The time complexity of the heuristic and its performance in comparison with well-established techniques are analyzed. The authors also present a graph comparing the lengths of minimum spanning trees to that of the Steiner trees obtained by the heuristic for different values of N. Some possible improvements and variations of the algorithm are suggested