A Short Review on Novel Approaches for Maximum Clique Problem: from Classical algorithms to Graph Neural Networks and Quantum algorithms

TL;DR

This paper reviews classical, neural network, and quantum algorithms for the Maximum Clique Problem, highlighting recent advances and benchmarking efforts across different approaches.

Contribution

It provides a comprehensive overview of traditional and cutting-edge methods, including graph neural networks and quantum algorithms, for solving the Maximum Clique Problem.

Findings

Classical algorithms are well-established for the problem.

Recent neural network approaches show promising results.

Quantum algorithms are emerging as a potential solution.

Abstract

This manuscript provides a comprehensive review of the Maximum Clique Problem, a computational problem that involves finding subsets of vertices in a graph that are all pairwise adjacent to each other. The manuscript covers in a simple way classical algorithms for solving the problem and includes a review of recent developments in graph neural networks and quantum algorithms. The review concludes with benchmarks for testing classical as well as new learning, and quantum algorithms.