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

Abstract

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.

X-architecture Steiner minimal tree algorithm based on multi-strategy optimization discrete differential evolution

“…In Liu et al (2011), Rectilinear Steiner Minimal Tree (RSMT) based on Discrete Particle Swarm Optimization (DPSO) algorithm was proposed to effectively optimize the average wire length (Liu et al, 2011). Liu et al (2014a) proposed a multi-layer obstacle avoidance RSMT construction method based on geometric reduction method (Liu et al, 2014a). Zhang, Ye & Guo (2016) proposed a heuristic for constructing a RSMT with slew constraints to maximize routing resources over obstacles (Zhang, Ye & Guo, 2016).…”