Abstract
In this paper, the 3-dimensional DNA graph structures model is used to solve the maximum clique problem. Based on the fact that the induced graph of a clique is complete, vertices building blocks are designed by k-armed DNA molecules and hairpin structures and the connecting structures are presented by 2-armed DNA structures so that they can spontaneously form into a 3-dimensional DNA graph structure with no cleaved ends if a clique were formed right by these vertices. Therefore the maximum clique is detected by finding the biggest complete graph. Theoretically, the algorithm designed here can generate initial data pool within polynomial steps and it takes constant number of steps to find the maximum clique.
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Acknowledgments
This work was supported by National Natural Science Foundation of China (61170038), Shandong Province Natural Science Foundation (ZR2011FM001), Humanities and Social Sciences project of Ministry of Education (12YJA630152).
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Ren, X., Liu, X. (2013). Three Dimensional DNA Graph Structure Solution to Maximum Clique Problem. In: Lu, W., Cai, G., Liu, W., Xing, W. (eds) Proceedings of the 2012 International Conference on Information Technology and Software Engineering. Lecture Notes in Electrical Engineering, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34522-7_11
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DOI: https://doi.org/10.1007/978-3-642-34522-7_11
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