Nearly Optimal Steiner Trees using Graph Neural Network Assisted Monte Carlo Tree Search

TL;DR

This paper introduces a novel approach combining graph neural networks with Monte Carlo Tree Search to compute Steiner Trees more effectively, often surpassing traditional algorithms and sometimes finding optimal solutions.

Contribution

It presents a new method that integrates GNNs with MCTS for Steiner Tree computation, achieving better results than standard approximation algorithms.

Findings

Outperforms the 2-approximation algorithm on various graphs

Often finds the optimal Steiner Tree

Demonstrates effectiveness across different graph types

Abstract

Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by combining a graph neural network and Monte Carlo Tree Search. We first train a graph neural network that takes as input a partial solution and proposes a new node to be added as output. This neural network is then used in a Monte Carlo search to compute a Steiner tree. The proposed method consistently outperforms the standard 2-approximation algorithm on many different types of graphs and often finds the optimal solution.