For the obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem, we present a Steiner-point-based algorithm that achieves the best practical performance among existing heuristics. We first propose a new concept of Steiner point locations, creating a linear-space routing graph with satisfactory Steiner point candidates to resolve the bottleneck of most existing heuristics. Then, we propose a Steiner-point-based framework to yield a solution, which is close to the key to the handling of the OARSMT problem. Experimental results show that this algorithm achieves excellent solution quality and speed performance at the same time. We also extend the Steiner-point-based framework to the obstacle-avoiding preferred direction Steiner tree problem with a good performance.

For the obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem, this paper presents a Steiner-point based algorithm to achieve the best practical performance in wirelength and run time. Unlike many previous works, the Steiner-based framework is more focused on the usage of Steiner points instead of the handling of obstacles. This paper also proposes a new concept of Steiner point locations to provide an effective as well as efficient way to generate desirable Steiner point candidates. Experimental results show that this algorithm achieves the best solution quality in Θ (n log n) empirical time, which was originally generated by applying the maze routing on an Ω(n2)-space graph. The Steiner-point based framework and the new concept of Steiner point locations can be applied to future research on the OARSMT problem and its generations, such as the multi-layer OARSMT problem.