Journal of Global Optimization

, Volume 37, Issue 1, pp 95–111

An Efficient Branch-and-bound Algorithm for Finding a Maximum Clique with Computational Experiments

Original Paper

DOI: 10.1007/s10898-006-9039-7

Cite this article as:
Tomita, E. & Kameda, T. J Glob Optim (2007) 37: 95. doi:10.1007/s10898-006-9039-7


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


Maximum cliqueAlgorithmBranch-and-boundApproximate coloringComputational experiments

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of Information and Communication EngineeringThe University of Electro-CommunicationsTokyoJapan