An improved bit parallel exact maximum clique algorithm

This paper describes new improvements for BB-MaxClique (San Segundo et al. in Comput Oper Resour 38(2):571–581, 2011), a leading maximum clique algorithm which uses bit strings to efficiently compute basic operations during search by bit masking. Improvements include a recently described recoloring strategy in Tomita et al. (Proceedings of the 4th International Workshop on Algorithms and Computation. Lecture Notes in Computer Science, vol 5942. Springer, Berlin, pp 191–203, 2010), which is now integrated in the bit string framework, as well as different optimization strategies for fast bit scanning. Reported results over DIMACS and random graphs show that the new variants improve over previous BB-MaxClique for a vast majority of cases. It is also established that recoloring is mainly useful for graphs with high densities.

[1]  Boris Goldengorin,et al.  Handbook of combinatorial optimization , 2013 .

[2]  Cristian S. Calude,et al.  Discrete Mathematics and Theoretical Computer Science , 2003, Lecture Notes in Computer Science.

[3]  Tatsuya Akutsu,et al.  Point matching under non-uniform distortions and protein side chain packing based on an efficient maximum clique algorithm. , 2002, Genome informatics. International Conference on Genome Informatics.

[4]  Janez Konc,et al.  An improved branch and bound algorithm for the maximum clique problem , 2007 .

[5]  P. Pardalos,et al.  An exact algorithm for the maximum clique problem , 1990 .

[6]  Gerhard J. Woeginger,et al.  Operations Research Letters , 2011 .

[7]  Shinya Takahashi,et al.  A Simple and Faster Branch-and-Bound Algorithm for Finding a Maximum Clique , 2010, WALCOM.

[8]  Patric R. J. Östergård,et al.  A fast algorithm for the maximum clique problem , 2002, Discret. Appl. Math..

[9]  David R. Wood,et al.  An algorithm for finding a maximum clique in a graph , 1997, Oper. Res. Lett..

[10]  Pablo San Segundo,et al.  Fast exact feature based data correspondence search with an efficient bit-parallel MCP solver , 2010, Applied Intelligence.

[11]  Etsuji Tomita,et al.  An Efficient Branch-and-Bound Algorithm for Finding a Maximum Clique , 2003, DMTCS.

[12]  Panos M. Pardalos,et al.  Handbook of combinatorial optimization. Supplement , 2005 .

[13]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[14]  P. Pardalos,et al.  Handbook of Combinatorial Optimization , 1998 .

[15]  Pablo San Segundo,et al.  An exact bit-parallel algorithm for the maximum clique problem , 2011, Comput. Oper. Res..

[16]  Wilbert E. Wilhelm,et al.  Clique-detection models in computational biochemistry and genomics , 2006, Eur. J. Oper. Res..

[17]  Lutz Volkmann,et al.  Graphs having distance-n domination number half their order , 2002, Discret. Appl. Math..

[18]  Sharad Malik,et al.  Chaff: engineering an efficient SAT solver , 2001, Proceedings of the 38th Design Automation Conference (IEEE Cat. No.01CH37232).

[19]  David S. Johnson,et al.  Cliques, Coloring, and Satisfiability , 1996 .