Using modular decomposition technique to solve the maximum clique problem

TL;DR

This paper introduces a modular decomposition-based algorithm for exactly solving the weighted maximum clique problem, demonstrating competitive performance on benchmark graphs.

Contribution

It presents a novel recursive algorithm leveraging modular decomposition trees and new graph construction algorithms for the maximum clique problem.

Findings

Competitive results on DIMACS benchmarks

Effective recursive approach using modular decomposition

New algorithms for constructing graphs with modules

Abstract

In this article we use the modular decomposition technique for exact solving the weighted maximum clique problem. Our algorithm takes the modular decomposition tree from the paper of Tedder et. al. and finds solution recursively. Also, we propose algorithms to construct graphs with modules. We show some interesting results, comparing our solution with Ostergard's algorithm on DIMACS benchmarks and on generated graphs