Efficient Multilayer Obstacle-Avoiding Rectilinear Steiner Tree Construction Based on Geometric Reduction

Given a set of pin-vertices, an obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) connects all the pin-vertices possibly through Steiner points using vertical and horizontal segments with the minimal wirelength and without intersecting any obstacle. To deal with multiple routing layers and preferred routing orientations, we consider the multilayer obstacle-avoiding rectilinear Steiner minimal tree (ML-OARSMT) problem and the obstacle-avoiding preferred direction Steiner tree (OAPD-ST) problem. First, we prove that the multilayer case is theoretically different from the 2D one, and propose a reduction to transform a multilayer instance into a 3D instance. Based on the reduction, we apply computational geometry techniques to develop an efficient algorithm, utilizing existing OARSMT heuristics, for the ML-OARSMT problem and the OAPD-ST problem. Furthermore, we develop an advanced Steiner point selection to avoid inferior Steiner points and to improve the solution quality. Experimental results show that our algorithm provides a solution with excellent quality and has a significant speed-up compared to previously known results.