MazeNet: An Accurate, Fast, and Scalable Deep Learning Solution for Steiner Minimum Trees

TL;DR

This work tackles the NP-hard Obstacle Avoiding Rectilinear Steiner Minimum Tree (OARSMT) problem by reframing it as image-based maze solving and solving it with MazeNet, a recurrent convolutional neural network. MazeNet learns to emulate iterative algorithms via RCNN blocks, augmented with a termination condition and progressive training, enabling generalization from small mazes to larger instances (up to 8 terminals) with 100% empirical accuracy and faster runtimes than exact approaches. The method incorporates parallelization for scalability on large inputs and demonstrates competitive performance against graph-approximation methods, highlighting a hybrid DL-and-algorithmic approach. The results suggest a promising direction for applying image-based learning to graph problems and point to future work on larger problems and graph-neural-network analogs.

Abstract

The Obstacle Avoiding Rectilinear Steiner Minimum Tree (OARSMT) problem, which seeks the shortest interconnection of a given number of terminals in a rectilinear plane while avoiding obstacles, is a critical task in integrated circuit design, network optimization, and robot path planning. Since OARSMT is NP-hard, exact algorithms scale poorly with the number of terminals, leading practical solvers to sacrifice accuracy for large problems. We propose MazeNet, a deep learning-based method that learns to solve the OARSMT from data. MazeNet reframes OARSMT as a maze-solving task that can be addressed with a recurrent convolutional neural network (RCNN). A key hallmark of MazeNet is its scalability: we only need to train the RCNN blocks on mazes with a small number of terminals; larger mazes can be solved by replicating the same pre-trained blocks to create a larger network. Across a wide range of experiments, MazeNet achieves perfect OARSMT-solving accuracy, significantly reduces runtime compared to classical exact algorithms, and can handle more terminals than state-of-the-art approximate algorithms.

Figures (15)

• Figure 1: A maze with three terminals (green squares), with an incorrect approximation solution that is not the minimum-length path (red), and the correct exhaustive solution (blue). The overlap between the solutions is shown in blue with red stripes.
• Figure 2: Example of converting a graph (a) to its corresponding maze (b), with the target image (c) as its shortest-path solution.
• Figure 3: Visualization of MazeNet's progress over time as it connects four terminals.
• Figure 4: Visualization of progress when a termination condition is needed to resolve between two almost equidistant paths, since otherwise MazeNet oscillates between them.
• Figure 5: Block diagram for MazeNet.