Abstract
In this paper a new algorithm that guarantees to enumerate all the existing cliques including the maximal clique based on set operations is presented. The first advantage of the algorithm is that it can be parallelized to improve the performance. The second being that it guarantees to find all the cliques. The algorithm cannot be considered as radically different from some of the existing algorithm except it uses simple set operation explicitly to find the cliques thus making the computation simpler. This also allows us to verify the results.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Brayton, R. K., Hachtel, G. D., Sangiovanni- Vincentelli, A. L., Multilevel Logic Synthesis, Proc. IEEE, Vol. 78, No. 2, February 1990, pp.264-300.
Balas, E., Yu, C. S., Finding a Maximal clique in an Arbitrary Graph, SIAM J. Computing 15(4), 1986, pp.1054-1068.
Biggs, N., Some Heuristics for Graph Coloring, in : R. Nelson and R. J. Wilson, eds, Graph Colourings, Longman, New York, 1990.
Bron, C., Kerbosch, J., Finding all Cliques of an Undirected Graph, Comm. ACM 16(9), 1973, pp. 575-577.
Carraghan, R., Pardalos, P. M., An Exact Algorithm for the Maximum Clique Problem, Operational Research Letters. 9, 1990, pp.375-382.
Franklin, M., Saluja, K. K., Hypergraph Coloring and Reconfigured RAM testing, IEEE Transactions on Computers, Vol. 43, No.6, June 1994, pp. 725-736.
Garey, M. R., Johnson, D. S., Computers and Interactability: A guide to the Theory of NP-Completeness, Freeman, 1979.
Lengauer, T., Combinatorial Algorithms for Integrated Circuit Layout, John Wiley & Sons, 1990.
Pardalos, P.M., Rappe, J., Resende, M.G.C., An Exact Parallel Algorithm for the Maximum Clique Problem, High Performance Algorithms and Software in Nonlinear Optimization, R. De Leone, Murl’i, P.M. Pardalos and G. Toraldo (eds.), Kluwer, Dordrecht, 1998, pp. 279-300.
Pardalos, P.M., Xue, J., The Maximum Clique Problem, J. Global Optimization, 4, 1994, pp. 301- 328.
Wood, D. R., An Algorithm for Finding a Maximum Clique in a Graph, Operational Research Letters, 21, 1997, pp. 211-217.
Tarjan, R. E., Trojanowski, A. E., Finding a Maximum Independent Set, SIAM J. Computing 6(3), 1977, pp. 537-546.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media B.V.
About this paper
Cite this paper
Bavan, A.S. (2008). A Parallel Algorithm that Enumerates all the Cliques in an Undirected Graph. In: Sobh, T. (eds) Advances in Computer and Information Sciences and Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8741-7_14
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8741-7_14
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8740-0
Online ISBN: 978-1-4020-8741-7
eBook Packages: Computer ScienceComputer Science (R0)