Quantum Algorithm for Finding a Maximum Clique in an Undirected GraphJournal: Journal of Information and Organizational Sciences (JIOS) (Vol.36, No. 2)
Publication Date: 2012-12-13
Authors : Alan Bojić;
Page : 91-98
Keywords : quantum computing; quantum algorithm; maximum clique;
The maximum clique in an undirected graph is the largest subset of a set of graph's vertices where each pair of elements in the subset is connected. In this paper I would like to propose an algorithm for quantum computers that finds a maximum clique in an arbitrary undirected graph. An algorithm has O(|V|2|V|/2) worst case time complexity and O(2|V|/2) best case time complexity. Algorithm's space complexity for each case is O(|V|). An algorithm is based on a version of Grover's quantum algorithm for finding element in an unsorted list in which there can be an unknown number of solutions.
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