Maximum Clique

The maximum clique problem (MCP) seeks the largest complete subgraph within a given graph, a fundamental challenge in computer science with applications ranging from social network analysis to robust map merging. Current research focuses on improving both exact and heuristic algorithms, including branching algorithms exploiting graph structure, evolutionary algorithms incorporating diversity and local search, and novel approaches using graph neural networks and even quantum computing. These efforts aim to overcome the inherent computational difficulty of MCP (NP-hardness) by developing faster and more accurate solutions, impacting diverse fields requiring efficient analysis of complex relationships.