As die sizes are shrinking, and circuit complexities are increasing, the PCB routing problem becomes more and more challenging. Traditional routing algorithms can not handle these challenges effectively, and many high-end designs in the industry require manual routing efforts. In this paper, we propose a problem decomposition that distinguishes routing within dense components from routing in the intermediate area. In particular, we propose an effective methodology to find the escape routing solution for multiple components simultaneously such that the number of crossings in the intermediate area is minimized. For this, we model the problem as a longest path with forbidden pairs (LPFP) problem, and propose two algorithms for it. The first is an exact polynomial-time algorithm that is guaranteed to find the maximal planar routing solution on one layer. The second is a randomized algorithm that has good scalability characteristics for large circuits. Then we use these algorithms to assign the maximal subset of planar nets to each layer, and then distribute the remaining nets at the end. We demonstrate the effectiveness of these algorithms through experiments on industrial circuits.