A heuristic for constructing a rectilinear Steiner tree by reusing routing resources over obstacles

The obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem is a hot topic in very-large-scale integration physical design. In practice, most of the obstacles occupy the device layer and certain lower metal layers. Therefore, we can place wires on top of the obstacles. To maximize routing resources over obstacles, we propose a heuristic for constructing a rectilinear Steiner tree with slew constraints. Our algorithm adopts an extended rectilinear full Steiner tree grid as the routing graph. We mark two types of Steiner point candidates, which are used for constructing Steiner trees and refining solutions. A shortest path heuristic variant is designed for constructing Steiner trees and it takes into account slew constraint by inhibiting growth. Furthermore, we use a pre-computed strategy to avoid calculating slew rate repeatedly. Experimental results show that our algorithm maximizes routing resources over obstacles and saves routing resources outside obstacles. Compared with the conventional OARSMT algorithm, our algorithm reduces the wire length outside obstacles by as much as 18.74% and total wire length by as much as 6.03%. Our algorithm improves the latest related algorithm by approximately 2% in terms of wire length within a reasonable running time. Additionally, calculating the slew rate only accounts for approximately 15% of the total runing time.     

Obstacle-avoiding rectilinear Steiner tree construction in sequential and parallel approach

The Rectilinear Steiner Minimum Tree (RSMT) problem is a fundamental one in VLSI physical design. In this paper, we present a maze routing based heuristics to solve the obstacle-avoiding RSMT (OARSMT) problem. Our approach can handle multi-pin nets in good quality and reasonable running time. We also present an implementation of the heuristics in parallel approach with the aid of graphic processing units (GPU). The parallel algorithm is implemented by using CUDA and has been tested on a NVIDIA graphic card. Our experimental results show that our parallel algorithm has promising speedups over our sequential approach. This work demonstrates that we can apply a parallel algorithm to solve the OARSMT problem with the aid of GPU.