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Efficient Algorithms for Finding Maximum and Maximal Cliques and Their Applications

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WALCOM: Algorithms and Computation (WALCOM 2017)

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Abstract

The problem of finding a maximum clique or enumerating all maximal cliques is very important and has been explored in several excellent survey papers. Here, we focus our attention on the step-by-step examination of a series of branch-and-bound depth-first search algorithms: Basics, MCQ, MCR, MCS, and MCT. Subsequently, as with the depth-first search as above, we present our algorithm, CLIQUES, for enumerating all maximal cliques. Finally, we describe some of the applications of the algorithms and their variants in bioinformatics, data mining, and other fields.

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Acknowledgments

The author would like to express his sincere gratitude to H. Ito, T. Akutsu, M. Haraguchi, Y. Okubo, T. Nishino, H. Takahashi and many others for their fruitful joint work and kind help. This work was supported by JSPS KAKENHI Grant Numbers JP16300001, JP19300040, JP19500010, JP21300047, JP22500009, JP25330009, Kayamori Foundation of Informational Science Advancement, Funai Foundation for Information Technologies, and others.

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  1. The Advanced Algorithms Research Laboratory, The University of Electro-Communications, Chofugaoka 1-5-1, Chofu, Tokyo, 182-8585, Japan

    Etsuji Tomita

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  1. Etsuji Tomita
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Correspondence to Etsuji Tomita .

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  1. Universiti Teknologi Brunei, Bandar Seri Begawan, Brunei Darussalam

    Sheung-Hung Poon

  2. Bangladesh University of Engineering and Technology, Dhaka, Bangladesh

    Md. Saidur Rahman

  3. National Taiwan University, Taipei, Taiwan

    Hsu-Chun Yen

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Tomita, E. (2017). Efficient Algorithms for Finding Maximum and Maximal Cliques and Their Applications. In: Poon, SH., Rahman, M., Yen, HC. (eds) WALCOM: Algorithms and Computation. WALCOM 2017. Lecture Notes in Computer Science(), vol 10167. Springer, Cham. https://doi.org/10.1007/978-3-319-53925-6_1

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  • DOI: https://doi.org/10.1007/978-3-319-53925-6_1

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