Sticker model is one of the basic models in the DNA computer models. This model is coded with single-double stranded DNA molecules. It has the following advantages that the operations require no strands extension and use no enzymes; What’s more, the materials are reusable. Therefore, it arouses attention and interest of scientists in many fields. In this paper, we extend and improve the sticker model, which will be definitely beneficial to the construction of DNA computer. This paper is the second part of our series paper, which mainly focuses on the application of sticker model. It mainly consists of the following three sections: the matrix representation of sticker model is first presented; then a brief review of the past research on graph and combinatorial optimization, such as the minimal set covering problem, the vertex covering problem, Hamiltonian path or cycle problem, the maximal clique problem, the maximal independent problem and the Steiner spanning tree problem, is described; Finally a DNA algorithm for the graph isomorphic problem based on the sticker model is given.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Xu, J., Dong, Y. F., Wei, X. P., Sticker DNA computer model, Part I: Theory, Chinese Science Bulletin, 2004, 49(8): 772–780.
Roweis, S., Winfree, E., Burgoyne, R. et al., A sticker based archtecture for DNA computation, DNA Based Computers (eds. Baum, E. B., Lipton, R. J.), Proc. 2nd Annual Meeting, Princeton, 1999, 1–27.
Gao Lin, Xu Jin, DNA solution of vertex cover problem based on sticker model, Chinese Journal of Electronics, 2002, 11(2): 280–284.
Braich, R. S., Chelyapov, N., Cliff, J. et al., Solution of a 20-variable 3-SAT problem on a DNA computer, Sci., 2002, 296(19): 499–502.
Zimmermann, K., Efficient DNA sticker algorithms for NP-complete graph problems, Computer Physics Communications, 2002, 144: 297–309.
Bondy, J. A., Murty, U. S. R., Graph Theory with Applications, London, Basingtoke and New York: The Macmillan Press LTD, 1976.
Papadimitriou, C. H., Steiglitz, K., Combinatorial Optimization: Algorithms and Complexity, Englewood Cliffs, N J: Prentice Hall, 1982, 358–409
Tinhofer, G., Computational Graph Theory, Vienna: Springer-Verlag, 1990.
Golumbic, M. C., Algorithmic Graph Theory and Perfect Graphs, New York: Academic Press, 1980.
Vinnakota, B., Andrews, J., Repair of RAMs with clustered faults, Proc. Int’l Conf. Computer-Aided-Design, New York: Academic Press, 1992: 582–585.
Paias, A., Paixao, J., State space relaxation for set covering problem related to bus driver scheduling, Eur. J. Opl. Res., 1993, 71: 303–316.
Beasley, J. E., Jornsten, K., Enhancing an algorithm for set covering problems, Eur. J. Opl. Res., 1992, 58: 293–300.
Lorena, L. A. N., Belo, L. F., A surrogate heuristics for set covering problems, Eur. J. Opl. Res., 1994, 79: 138–150.
Fisher, M. L., Kedia, D., Optimal solution of set covering /partitioning problems using dual heuristics, Mgmt Sci., 36: 674–688.
Naft, J., Neuropt: Neurocomputing for multiobjective design optimization for printed circuit board component, Proc., Joint Conf. Neural Networks, 1989, 503–506.
Xu, J., Bao, Z., Neural networks and graph theory, Science in China, Ser. E, 2001, 31(6): 533–555.
Adleman, L. M., Molecular computation of solutions to combinatorial problems, Science, 1994, 266(11): 1021–1023.
Lipton, R. J., DNA solution of hard computational problems, Science, 1995, 268(28): 542–545.
Cukras, A. R., Faulhammer, D., Lipton, R. J. et al., Chess games: A model for RNA-based computation, Biosystems, 1999, 52; 35–45.
Sakamoto, K., Gouzu, H., Komiya, K. et al., Molecular computation by DNA hairpin formation, Science, 2000, 288: 1223–1226.
Liu, Q. H., Wang, L. M., Frutos, A. G. et al., DNA computing on surfaces, Nature, 2000, 403: 175–179.
Faulhammer, D., Cukras, A. R., Lipton, R. J. et al., Molecular computation: RNA solutions to chess problems, Biochemistry, 2000, 97(4): 1385–1389.
Yin, Z. X., Zhang, F. Y., Xu, J., DNA computing based on molecular beacons, J. of Biomathematics, 2003, 18(4): 1–5.
Xu, J., Self-Complementary Graph Theory with Applications (in Chinese), Xi’an: Xidian University publishing company, 1999.
Hwang, F. K., Richards, D. S., Winter, P., The Steiner Tree Problem, New York: Elsevier Science Publishers B.V. Press, 1992.
Xu, J., Zhang, J. Y., Bao, Z., Algorithm for the isomorphism of graphs based on hopfield networks, Journal of Electronics (Supplement), 1996, 116–121.
About this article
Cite this article
Xu, J., Li, S., Dong, Y. et al. Sticker DNA computer model — Part II: Application. Chin. Sci. Bull. 49, 863–871 (2004). https://doi.org/10.1007/BF03183999
- DNA computing
- sticker model
- k-bit sticker model
- combinatorial optimization problem