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 ( n  3 ) 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.
['Chih-Hung Liu', 'Shih-Yi Yuan', 'Sy-Yen Kuo', 'Yao-Hsin Chou']
An O(n log n) path-based obstacle-avoiding algorithm for rectilinear Steiner tree construction