Quantum Algorithm for Finding a Maximum Clique in an Undirected Graph
<p class="Abstract">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 ar...
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| Format: | Article |
| Language: | English |
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University of Zagreb, Faculty of organization and informatics
2012-12-01
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| Series: | Journal of Information and Organizational Sciences |
| Subjects: | |
| Online Access: | http://jios.foi.hr/index.php/jios/article/view/624 |
| Summary: | <p class="Abstract">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<sup>|V|/2</sup>) worst case time complexity and O(2<sup>|V|/2</sup>) 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.</p> |
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| ISSN: | 1846-3312 1846-9418 |