An O(n log n) path-based obstacle-avoiding algorithm for rectilinear Steiner tree construction

For the obstacle-avoiding rectilinear Steiner minimal tree problem, this paper presents an O(n log n)-time algorithm with theoretical optimality guarantees on a number of specific cases, which required O(n³) time in previous works. We propose a new framework to directly generate O(n) critical paths as essential solution components, and prove that those paths guarantee the existence of desirable solutions. The path-based framework neither generates invalid initial solutions nor constructs connected routing graphs, and thus provides a new way to deal with the OARSMT problem. Experimental results show that our algorithm achieves the best speed performance, while the average wirelength of the resulting solutions is only 1.1% longer than that of the best existing solutions.