Abstract
The maximum clique problem is to find the largest set of pairwise adjacent vertices in a graph. The problem has been shown to be \(\mathcal {N}\mathcal {P}\)-hard. This paper presents an approach to solve the maximum clique problem based on a constructive genetic algorithm that uses a combination of deterministic and stochastic moves. The problem has wide applications in areas such as bioinformatics, experimental analysis, information retrieval, signal transmission, and computer vision. The algorithm was implemented and tested on DIMACS benchmarks. Favorable results are reported.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Garey, M.R., Johnson, D.S.: Computers, Complexity, and Intractability. W. H. Freeman and Co, San Francisco (1979)
Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti-Spaccamela, A., Protasi, M.: Complexity and approximation: combinatorial optimization problems and their approximability properties. Springer, Berlin (2000)
Gavril, F.: Algorithms for minimum coloring, maximum clique, minimum covering by cliques, and maximum independent set of a chordal graph. SIAM J. Comput. 1, 180–187 (1972)
Harary, F., Ross, I.: A procedure for clique detection using the group matrix. Sociometry 20(3), 205–215 (1957)
Bron, C., Kerbosch, J.: Algorithm 457: finding all cliques of an undirected graph. Commun. ACM 16(9), 575–577 (1973)
Tomita, E., Tanaka, A., Takahashi, H.: The worst-case time complexity for generating all maximal cliques and computational experiments. Theor. Comput. Sci. 363, 28–42 (2006)
Alusaifeer, T., Ramanna, S., Henry, C.J., Peters, J.: GPU implementation of MCE approach to finding near neighbourhoods. In: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2013)
Balas, E., Yu, C.S.: Finding a maximum clique in an arbitrary graph. SIAM J. Comput. 15(4), 1054–1068 (1986)
Feo, T.A., Resende, M.G.C.: A greedy randomized adaptive search procedure for maximum independent set. Oper. Res. 42, 860–878 (1994)
Homer, S., Peinado, M.: Experiments with polynomial-time CLIQUE approximation algorithms on very large graphs. In: Johnson, D., Trick, M. (eds.), Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, pp. 147–167. American Mathematical Society, Providence (1996)
Jagota, A.: Adaptive, restart, randomized greedy heuristics for maximum clique. J. Heuristics 7(21), 565–585 (2001)
Ouyang, Q., Kaplan, P.D., Liu, S., Libchaber, A.: DNA solution of the maximal clique problem. Science 278, 446–449 (1997)
Ji, Y., Xu, X., Stormo, G.D.: A graph theoretical approach for predicting common RNA secondary structure motifs including pseudoknots in unaligned sequences. Bioinformatics 20, 1591–602 (2004)
Bui, T.N., Eppley, P.H.: A hybrid genetic algorithm for the maximum clique problem. In: Proceedings of the 6th International Conference on Genetic Algorithms, pp. 478–484 (1995)
Fleurent, C., Ferland, J.: Object-oriented implementation of heuristic search methods for graph coloring, maximum clique, and satisfiability. In: Johnson, D.S., Trick, M. (eds.) Cliques, Coloring, and Satisfiability: Second DIMACS Implementation Challenge, DIMACS Series in Discrete Mathematics and Theoretical Computer Science. American Mathematical Society, Providence (1996)
Marchiori, E.: A simple heuristic based genetic algorithm for the maximum clique problem. In: Proceedings of the 1998 ACM Symposium on Applied Computing – SAC’98 (1998)
Trefftz, C., Santamaria-Galvis, A., Cruz, R.: Parallelizing an algorithm to find the maximal clique on interval graphs on graphical processing units. In: IEEE International Conference on Electro Information Technology (2014)
Dekel, E., Sahni, S.: Parallel scheduling algorithms. Oper. Res. 31(1), 24–49 (1983)
Goldberg, D.E., Holland, J.H.: Machine Learning 3, 95 (1988)
Second DIMACS Challenge on Cliques, Coloring and Satisfiability: http://iridia.ulb.ac.be/~scia/maximum_clique/DIMACSbenchmark (1993)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Moussa, R., Akiki, R., Harmanani, H. (2019). A Genetic Algorithm for the Maximum Clique Problem. In: Latifi, S. (eds) 16th International Conference on Information Technology-New Generations (ITNG 2019). Advances in Intelligent Systems and Computing, vol 800. Springer, Cham. https://doi.org/10.1007/978-3-030-14070-0_80
Download citation
DOI: https://doi.org/10.1007/978-3-030-14070-0_80
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-14069-4
Online ISBN: 978-3-030-14070-0
eBook Packages: EngineeringEngineering (R0)