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

TL;DR

MazeNet introduces a deep learning approach that effectively solves the obstacle avoiding rectilinear Steiner minimum tree problem, achieving high accuracy and scalability, outperforming traditional algorithms in speed and size handling.

Contribution

MazeNet is the first deep learning model that reframes OARSMT as a maze-solving task, enabling scalable and accurate solutions for large problems by reusing trained modules.

Findings

MazeNet achieves perfect accuracy on OARSMT instances.

It significantly reduces runtime compared to classical algorithms.

It can handle more terminals than existing approximate methods.

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.