Abstract
We present a depth-first search algorithm for generating all maximal cliques of an undirected graph, in which pruning methods are employed as in Bron and Kerbosch’s algorithm. All maximal cliques generated are output in a tree-like form. Then we prove that its worst-case time complexity is O(3n/3) for an n-vertex graph. This is optimal as a function of n, since there exist up to 3n/3 cliques in an n-vertex graph.
This research has been supported in part by Grants-in-Aid for Scientific Research Nos. 13680435 and 16300001 from the Ministry of Education, Culture, Sports, Science and Technology, Japan, and Research Fund of the University of Electro-Communications. It is also given a grant by Funai Foundation for Information Technology.
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Tomita, E., Tanaka, A., Takahashi, H. (2004). The Worst-Case Time Complexity for Generating All Maximal Cliques. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_19
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DOI: https://doi.org/10.1007/978-3-540-27798-9_19
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