  A clique in an undirected graph G= (V, E) is a subset V' V of vertices, each
pair of which is connected by an edge in E. The clique problem is an
optimization problem of finding a clique of maximum size in graph. The clique
problem is NP-Complete. We have succeeded in developing a fast algorithm for
maximum clique problem by employing the method of verification and elimination.
For a graph of size N there are 2N sub graphs, which may be cliques and hence
verifying all of them, will take a long time. Idea is to eliminate a major
number of sub graphs, which cannot be cliques and verifying only the remaining
sub graphs. This heuristic algorithm runs in polynomial time and executes
successfully for several examples when applied to random graphs and DIMACS
benchmark graphs.
