Journal of Applied Mathematics

Solving Vertex Cover Problem Using DNA Tile Assembly Model

Zhihua Chen, Tao Song, Yufang Huang, and Xiaolong Shi

Full-text: Open access

Abstract

DNA tile assembly models are a class of mathematically distributed and parallel biocomputing models in DNA tiles. In previous works, tile assembly models have been proved be Turing-universal; that is, the system can do what Turing machine can do. In this paper, we use tile systems to solve computational hard problem. Mathematically, we construct three tile subsystems, which can be combined together to solve vertex cover problem. As a result, each of the proposed tile subsystems consists of Θ(1) types of tiles, and the assembly process is executed in a parallel way (like DNA’s biological function in cells); thus the systems can generate the solution of the problem in linear time with respect to the size of the graph.

Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 407816, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808287

Digital Object Identifier
doi:10.1155/2013/407816

Mathematical Reviews number (MathSciNet)
MR3142564

Zentralblatt MATH identifier
06950654

Citation

Chen, Zhihua; Song, Tao; Huang, Yufang; Shi, Xiaolong. Solving Vertex Cover Problem Using DNA Tile Assembly Model. J. Appl. Math. 2013 (2013), Article ID 407816, 7 pages. doi:10.1155/2013/407816. https://projecteuclid.org/euclid.jam/1394808287


Export citation

References

  • L. M. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, vol. 266, no. 5187, pp. 1021–1024, 1994.
  • E. Winfree, Algorithmic self-assembly of DNA [Ph.D. thesis], California Institute of Technology, Pasadena, Calif, USA, 1998.
  • J. H. Reif, S. Sahu, and P. Yin, “Compact error-resilient computational DNA tiling assemblies,” in Proceedings of the 10th International Workshop on DNA Computing, pp. 293–307, June 2004.
  • P. W. K. Rothemund, N. Papadakis, and E. Winfree, “Algorithmic self-assembly of DNA sierpinski triangles,” PLoS Biology, vol. 2, no. 12, 2004.
  • G. Pǎun, Membrane Computing: an Introduction, Springer, Berlin, Germany, 2002.
  • G. Pǎun, G. Rozenberg, and A. Salomaa, Eds., The Oxford Handbook of Membrane Computing, Oxford University Press, 2010.
  • G. Pǎun, “Computing with membranes,” Journal of Computer and System Sciences, vol. 61, no. 1, pp. 108–143, 2000.
  • T. Song, L. Pan, K. Jiang, B. Song, and W. Chen, “Normal forms for some classes of sequential spiking neural P systems,” IEEE Transactions on Nanobioscience, vol. 12, no. 3, pp. 255–264, 2013.
  • J. Wang, H. J. Hoogeboom, L. Pan, G. Pǎun, and M. J. Pérez-Jiménez, “Spiking neural P systems with weights,” Neural Computation, vol. 22, no. 10, pp. 2615–2646, 2010.
  • T. Song, L. Pan, J. Wang, I. Venkat, K. G. Subramanian, and R. Abdullah, “Normal forms of spiking neural P systems with anti-spikes,” IEEE Transactions on NanoBioscience, vol. 11, no. 4, pp. 352–359, 2012.
  • L. Pan and G. Pǎun, “Spiking neural P systems: an improved normal form,” Theoretical Computer Science, vol. 411, no. 6, pp. 906–918, 2010.
  • T. Song, L. Pan, and G. Pǎun, “Asynchronous spiking neural P systems with local synchronization,” Information Sciences, vol. 219, pp. 197–207, 2012.
  • L. Adleman, P. K. M. Rothemund, S. Roweis, and E. Winfree, “On applying molecular computation to the data encryption standard,” in Proceedings of the 2nd Annual Meeting on DNA Computers, pp. 10–12, Princeton, NJ, USA, 1996.
  • R. S. Braich, N. Chelyapov, C. Johnson, P. W. K. Rothemund, and L. Adleman, “Solution of a 20-variable 3-SAT problem on a DNA computer,” Science, vol. 296, no. 5567, pp. 499–502, 2002.
  • J.-M. Lehn, “Supramolecular chemistry,” Science, vol. 260, no. 5115, pp. 1762–1763, 1993.
  • C. Mao, T. H. LaBean, J. H. Reif, and N. C. Seeman, “Logical computation using algorithmic self-assembly of DNA triple-crossover molecules,” Nature, vol. 407, no. 6803, pp. 493–496, 2000.
  • R. D. Barish, P. W. K. Rothemund, and E. Winfree, “Two computational primitives for algorithmic self-assembly: copying and counting,” Nano Letters, vol. 5, no. 12, pp. 2586–2592, 2005.
  • P. Rothemund and E. Winfree, “The program-size complexity of self-assembled squares,” in Proceedings of ACM Symposium on Theory of Computing (STOC '02), pp. 459–468, Quebec, Canad, May 2000.
  • Y. Brun, “Arithmetic computation in the tile assembly model: addition and multiplication,” Theoretical Computer Science, vol. 378, no. 1, pp. 17–31, 2007.