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A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique

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WALCOM: Algorithms and Computation (WALCOM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5942))

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Abstract

This paper proposes new approximate coloring and other related techniques which markedly improve the run time of the branch-and-bound algorithm MCR (J. Global Optim., 37, 95–111, 2007), previously shown to be the fastest maximum-clique-finding algorithm for a large number of graphs. The algorithm obtained by introducing these new techniques in MCR is named MCS. It is shown that MCS is successful in reducing the search space quite efficiently with low overhead. Consequently, it is shown by extensive computational experiments that MCS is remarkably faster than MCR and other existing algorithms. It is faster than the other algorithms by an order of magnitude for several graphs. In particular, it is faster than MCR for difficult graphs of very high density and for very large and sparse graphs, even though MCS is not designed for any particular type of graphs. MCS can be faster than MCR by a factor of more than 100,000 for some extremely dense random graphs.

This research was supported in part by Grants-in-Aid for Scientific Research Nos. 16300001, 19500010, and 21300047 from the Ministry of Education, Culture, Sports, Science and Technology, Japan. It was also partially supported by a Special Grant for the Strategic Information and Communications R&D Promotion Programme (SCOPE) Project from the Ministry of Internal Affairs and Communications, Japan.

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Authors and Affiliations

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

    Etsuji Tomita, Yoichi Sutani, Takanori Higashi, Shinya Takahashi & Mitsuo Wakatsuki

Authors
  1. Etsuji Tomita
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  2. Yoichi Sutani
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  3. Takanori Higashi
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  4. Shinya Takahashi
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  5. Mitsuo Wakatsuki
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, Bangladesh University of Engineering and Technology (BUET), 1000, Dhaka, Bangladesh

    Md. Saidur Rahman

  2. Graduate School of Engineering, Department of Information Engineering, Hiroshima University, Kagamiyama 1-4-1, 739-8527, Higashi-Hiroshima, Japan

    Satoshi Fujita

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Tomita, E., Sutani, Y., Higashi, T., Takahashi, S., Wakatsuki, M. (2010). A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique. In: Rahman, M.S., Fujita, S. (eds) WALCOM: Algorithms and Computation. WALCOM 2010. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11440-3_18

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  • DOI: https://doi.org/10.1007/978-3-642-11440-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11439-7

  • Online ISBN: 978-3-642-11440-3

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