Before revision: In the Maximum Clique Problem, the objective is to find a clique whose size is maximum among all the cliques of an arbitrary undirected and unweighted graph. Maximum Clique Problem resembles with minimum vertex cover problem , independent set problem. As it is an NP-hard problem, no polynomial time algorithms can be found. As these problems have several important practical applications such as information retrieval, community detection in network, spatial data mining etc, it is of great interest to try to synthesis the circuit of Maximum Clique Problem. In classical computing any brute-force solution to the Maximum Clique Problem requires an exponential increase of time with the size of the problem (i.e., with time complexity of O(2^n)) . In this paper, Maximum Clique Problem has been solved using combinatorial approachof Grover's search algorithm .
After revision: Clique problem has several applications in computer vision, automatic test pattern generation, predicting protein structures, and many kinds of such pattern search . In this paper, Maximum Clique Problem has been solved using combinatorial approachof Grover's search algorithm .