Estimating the stability number of a random graph using convolutional neural networks

TL;DR

This paper investigates using convolutional neural networks on graph images to predict the stability number of random graphs, demonstrating potential for deep learning in complex combinatorial optimization tasks.

Contribution

It introduces a novel approach of applying CNNs to graph image representations for estimating the stability number, a previously challenging combinatorial property.

Findings

CNNs can predict the stability number from graph images.

Deep learning shows promise for combinatorial optimization problems.

The method offers a new tool for graph property estimation.

Abstract

Graph combinatorial optimization problems are widely applicable and notoriously difficult to compute; for example, consider the traveling salesman or facility location problems. In this paper, we explore the feasibility of using convolutional neural networks (CNNs) on graph images to predict the cardinality of combinatorial properties of random graphs and networks. Specifically, we use image representations of modified adjacency matrices of random graphs as training samples for a CNN model to predict the stability number of random graphs; where the stability number is the cardinality of a maximum set of vertices in a graph that contains no pairwise adjacency between vertices. The model and results presented in this study suggest potential for applying deep learning in combinatorial optimization problems previously not considered by simple deep learning techniques.