An Efficient Branch-and-Bound Algorithm for Finding a Maximum Clique

  • Etsuji Tomita
  • Tomokazu Seki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2731)


We present an exact and efficient branch-and-bound algorithm for finding a maximum clique in an arbitrary graph. The algorithm is not specialized for any particular kind of graph. It employs approximate coloring and appropriate sorting of vertices to get an upper bound on the size of a maximum clique. We demonstrate by computational experiments on random graphs with up to 15,000 vertices and on DIMACS benchmark graphs that our algorithm remarkably outperforms other existing algorithms in general. It has been successfully applied to interesting problems in bioinformatics, image processing, the design of quantum circuits, and the design of DNA and RNA sequences for bio-molecular computation.


Search Space Random Graph Maximum Clique Quantum Circuit Sparse Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Etsuji Tomita
    • 1
  • Tomokazu Seki
    • 1
  1. 1.The Graduate School of Electro-CommunicationsThe University of Electro-CommunicationsTokyoJapan

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