An efficient branch-and-bound algorithm for finding a maximum clique

  • Authors:

  • Etsuji Tomita;Tomokazu Seki

  • Affiliations:

  • The Graduate School of Electro-Communications, The University of Electro-Communications, Tokyo, Japan;The Graduate School of Electro-Communications, The University of Electro-Communications, Tokyo, Japan

  • Venue:
  • DMTCS'03 Proceedings of the 4th international conference on Discrete mathematics and theoretical computer science
  • Year:
  • 2003

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Abstract

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 biomolecular computation.