Algorithms for Finding Maximal and Maximum Cliques: A Survey

Abstract

Finding maximal and maximum cliques are well-known problems in the graph theory. They have different applications in several fields such as the analysis of social network, bioinformatics and graph coloring. They have attracted the interest of the research community. The main goal of this paper is to present a comprehensive review of the existing approaches for finding maximal and maximum cliques. It presents a comparative study of the existing algorithms based on some criteria and identifies the critical challenges. Then, it aims to motivate the future development of more efficient algorithms.