Approximate Maximum Clique Algorithm (AMCA): A Clever Technique for Solving the Maximum Clique Problem through Near Optimal Algorithm for Minimum Vertex Cover Problem
Muhammad Fayaz, Shakeel Arshad, Abdul Salam Shah, Asadullah Shah · International Journal of Control and Automation · 2018
Background and Objective:The process of solving the Maximum Clique (MC) problem through approximation algorithms is harder, however, the Minimum Vertex Cover (MVC) problem can easily be solved using approximation algorithms.In this paper, a technique has been proposed to use the approximation algorithms of Minimum Vertex Cover (MVC) for the solution of the Maximum Clique (MC) problem. Materials and Methods:To test the proposed technique, selected approximation algorithms have been deployed to small graph instances.The algorithms that were used for experiments are Maximum Degree Greedy (MDG), Vertex Support Algorithm (VSA), Mean of Neighbors of Minimum Degree Algorithm (MNMA), Modified Vertex Support Algorithm (MVSA), Maximum Adjacent Minimum Degree Algorithm (MAMA), and Clever Steady Strategy Algorithm (CSSA).Results: The development of an efficient approximation algorithm for the Maximum Clique (MC) problem is very difficult due to its complex nature.The only way left is to use the approximation algorithm of Minimum Vertex Cover (MVC) for the solution of the Maximum Clique (MC) problem.The experimental analysis of the proposed algorithm has revealed that the Maximum Clique (MC) problem can be efficiently solved with approximation algorithms of Minimum Vertex Cover (MVC).The proposed algorithm has efficiently solved the Maximum Clique (MC) problem within the reduced time limit.Conclusions: It is a difficult task to directly solve the Maximum Clique (MC) problem through approximation algorithms.The proposed method provides a platform to efficiently solve the Maximum Clique (MC) problem by using the approximation algorithm of Minimum Vertex Cover (MVC).