Abstract
This paper presents an implementation of Croitoru’s genetic algorithm for graph coloring problem, and some necessary modification and simplifying are made by using DNA operations. In this algorithm, each vertex and edge is encoded with a series of encodings incorporating position information, and the initial diverse candidate population is generated using POA. One crossover operator, two mutation operators, evaluation and selection operators are all implemented using basic operations on DNA. It is shown that the algorithm can be implemented with space complexity much decreased and time complexity O(mn2) to get a new generation, where n is the number of vertices and m is the number of edges. Moreover, borrowing ideas from the above implementation, an algorithm for Maximal Clique problem is also presented.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Johnson, D.S., Aragon, C.R., McGeoch, L.A., Schevon, C.: Optimization by simulated annealing: An experimental evaluation: Part II, graph coloring and number partitioning. Operations Research 39(3), 378–406 (1991)
Croitoru, C., Luchian, H., Gheorghies, O., Apetrei, A.: A New Genetic Graph Coloring Heuristic. In: COLOR 2002, Ithaca, NY (2002)
Amos, M., Gibbons, A.: Error-resistant Implementation of DNA Computations. In: Proceedings of the Second Annual Meeting on DNA Based Computers, vol. 44, pp. 151–168 (1996)
Bach, E., Condon, A., Glaser, E., Tanguay, C.: DNA models and algorithms for NP-complete problems. In: Proceedings of 11th Conference on Computational Complexity, pp. 290–299. IEEE Computer Society Press, Los Alamitos (1996)
Adleman, L.: Molecular computation of solution to combinatorial problems. Science, 266, 1021–1024 (1994)
Cai, W., Condon, A., Corn, R., Glaser, E., Fei, Z., Frutos, T., Guo, Z., Lagally, M., Liu, Q., Smith, L., Thiel, A.: The power of surface-based DNA computation. In: Proceedings of 1st International Conference on Computational Molecular Biology, pp. 67–74. ACM Press, New York (1997)
DĂaz, S., Esteban, J.L., Ogihara, M.: A DNA-based random walk method for solving k-SAT. In: Condon, A., Rozenberg, G. (eds.) DNA 2000. LNCS, vol. 2054, pp. 209–220. Springer, Heidelberg (2001)
Stemmer, W.P.C.: The evolution of molecular computation. Science 270, 1510–1510 (1995)
Chen, J., Antipov, E., Lemieux, B., Cedeno, W., Wood, D.H.: DNA computing implementing genetic algorithms. In: Landweber, L.F., Winfree, E., Lipton, R., Freeland, S. (eds.) Evolution as Computation, pp. 39–49. Springer, New York (1999)
Rose, J., Takano, M., Suyama, A.: A PNA-mediated Whiplash PCR-based Program for In Vitro Protein Evolution. In: Hagiya, M., Ohuchi, A. (eds.) DNA 2002. LNCS, vol. 2568, pp. 47–60. Springer, Heidelberg (2003)
Chen, K., Ramachandran, V.: A Space Efficient Randomized DNA Algorithm. In: Condon, A., Rozenberg, G. (eds.) DNA 2000. LNCS, vol. 2054, pp. 199–208. Springer, Heidelberg (2001)
Ouyang, Q., Kaplan, P.D., Liu, S., Libechabe, A.: DNA Solution of the Maximal Clique Problem. Science 278, 446–449 (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liu, X., Yin, J., Jwo, JS., Feng, Z., Dong, J. (2005). A DNA-Based Genetic Algorithm Implementation for Graph Coloring Problem. In: Huang, DS., Zhang, XP., Huang, GB. (eds) Advances in Intelligent Computing. ICIC 2005. Lecture Notes in Computer Science, vol 3645. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11538356_11
Download citation
DOI: https://doi.org/10.1007/11538356_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28227-3
Online ISBN: 978-3-540-31907-8
eBook Packages: Computer ScienceComputer Science (R0)