The 1-Steiner tree problem in lambda-3 geometry plane

In this paper, we extend the 1-Steiner idea of Georgakopoulos and Papadimitriou [5] to the Steiner tree problem in lambda-3 geometry plane. Our extension to the lambda-3 geometry plane and that of Kahng and Robins [9] to the rectilinear plane are similar in principle, but different in many nontrivial details. After presenting an efficient algorithm for solving the 1-Steiner tree problem, we apply the iterated 1-Steiner heuristic to compute approximations to the Steiner minimum tree problem in lambda-3 geometry plane. Computational results on standard benchmarks show that our algorithm compares favorably with previously published heuristics.