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Maximum Degree Vertex-Based Algorithm for Maximum Clique Problem
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 Title & Authors
Maximum Degree Vertex-Based Algorithm for Maximum Clique Problem
Lee, Sang-Un;
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In this paper, I propose a linear time algorithm devised to produce exact solution to NP-complete maximum clique problem. The proposed algorithm firstly, from a given graph G=(V,E), sets vertex of the maximum degree as clique's major vertex. It then selects vertex of among vertices that are adjacent to , only to determine as candidate cliques w and . Next it obtains by sorting in the descending order. Lastly, the algorithm executes the same procedure on graph to compare newly attained cliques to previously attained cliques so as to choose the lower. With this simple method, multiple independent cliques would also be attainable. When applied to various regular and irregular graphs, the algorithm proposed in this paper has obtained exact solutions to all the given graphs linear time O(n).
Maximum clique;Degree;Maximum Degree;Candidate clique;
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