Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 275019, 8 pages
http://dx.doi.org/10.1155/2015/275019
Research Article

Solving the Maximum Weighted Clique Problem Based on Parallel Biological Computing Model

1School of Information Sciences, Shanghai Ocean University, Shanghai 201306, China
2Guangxi Institute of Water Resources Research, Nanning 530023, China
3State Key Laboratory of Simulation and Regulation of River Basin Water Cycle, China Institute of Water Resources and Hydropower Research, Beijing 100048, China
4Department of Civil Engineering, Xi’an University of Architecture & Technology, Xi’an 710055, China

Received 2 July 2014; Revised 15 September 2014; Accepted 20 September 2014

Academic Editor: L. W. Zhang

Copyright © 2015 Zhaocai Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. L. M. Adleman, “Molecular computation of solutions to combinatorial problems,” Science, vol. 266, no. 5187, pp. 1021–1024, 1994. View at Publisher · View at Google Scholar · View at Scopus
  2. R. J. Lipton, “DNA solution of hard computational problems,” Science, vol. 268, no. 5210, pp. 542–545, 1995. View at Publisher · View at Google Scholar · View at Scopus
  3. A. Fujiwara, K. Matsumoto, and W. Chen, “Procedures for logic and arithmetic operations with DNA molecules,” International Journal of Foundations of Computer Science, vol. 15, no. 3, pp. 461–474, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  4. W. X. Li, D. M. Xiao, and L. He, “DNA ternary addition,” Applied Mathematics and Computation, vol. 182, no. 2, pp. 977–986, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. F. Guarnieri, M. Fliss, and C. Bancroft, “Making DNA add,” Science, vol. 273, no. 5272, pp. 220–223, 1996. View at Publisher · View at Google Scholar · View at Scopus
  6. X. C. Liu, X. F. Yang, S. L. Li, and Y. Ding, “Solving the minimum bisection problem using a biologically inspired computational model,” Theoretical Computer Science, vol. 411, no. 6, pp. 888–896, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. G. Paun, G. Rozenberg, and A. Salomaa, DNA Computing, Springer, New York, NY, USA, 1998.
  8. J. Y. Lee, S.-Y. Shin, T. H. Park, and B.-T. Zhang, “Solving traveling salesman problems with DNA molecules encoding numerical values,” BioSystems, vol. 78, no. 1–3, pp. 39–47, 2004. View at Publisher · View at Google Scholar · View at Scopus
  9. X. L. Wang, Z. M. Bao, J. J. Hu, S. Wang, and A. Zhan, “Solving the SAT problem using a DNA computing algorithm based on ligase chain reaction,” BioSystems, vol. 91, no. 1, pp. 117–125, 2008. View at Publisher · View at Google Scholar · View at Scopus
  10. Z. Wang, D. Xiao, W. Li, and L. He, “A DNA procedure for solving the shortest path problem,” Applied Mathematics and Computation, vol. 183, no. 1, pp. 79–84, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. A. Brenneman and A. Condon, “Strand design for biomolecular computation,” Theoretical Computer Science, vol. 287, no. 1, pp. 39–58, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  12. M. Y. Guo, W.-L. Chang, M. Ho, J. Lu, and J. N. Cao, “Is optimal solution of every NP-complete or NP-hard problem determined from its characteristic for DNA-based computing,” BioSystems, vol. 80, no. 1, pp. 71–82, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Wang, T. Yang, Y. Ma et al., “Mathematical modeling and stability analysis of macrophage activation in left ventricular remodeling post-myocardial infarction,” BMC Genomics, vol. 13, supplement 6, article S21, 2012. View at Google Scholar · View at Scopus
  14. Y. Wang, H.-C. Han, J. Y. Yang, M. L. Lindsey, and Y. Jin, “A conceptual cellular interaction model of left ventricular remodelling post-MI: dynamic network with exit-entry competition strategy,” BMC Systems Biology, vol. 4, supplement 1, article S5, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. W.-L. Chang, “Fast parallel DNA-based algorithms for molecular computation: quadratic congruence and factoring integers,” IEEE Transactions on Nanobioscience, vol. 11, no. 1, pp. 62–69, 2012. View at Publisher · View at Google Scholar · View at Scopus
  16. Z. C. Wang, D. M. Huang, H. J. Meng, and C. P. Tang, “A new fast algorithm for solving the minimum spanning tree problem based on DNA molecules computation,” BioSystems, vol. 114, no. 1, pp. 1–7, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. Y. Xu and Z. Wang, “Genetic algorithm optimized CCEM for complex topology,” Mathematical Problems in Engineering, vol. 2012, Article ID 383248, 14 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  18. W.-L. Chang, M. S.-H. Ho, and M. Guo, “Fast parallel molecular algorithms for DNA-based computation: factoring integers,” IEEE Transactions on Nanobioscience, vol. 4, no. 2, pp. 149–163, 2005. View at Publisher · View at Google Scholar · View at Scopus
  19. Z. C. Wang, Y. M. Zhang, W. H. Zhou, and H. F. Liu, “Solving traveling salesman problem in the Adleman-Lipton model,” Applied Mathematics and Computation, vol. 219, no. 4, pp. 2267–2270, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. T. Yang, Y. A. Chiao, Y. Wang et al., “Mathematical modeling of left ventricular dimensional changes in mice during aging,” BMC Systems Biology, vol. 6, supplement 3, article S10, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. Z. C. Wang, J. Tan, D. M. Huang, Y. C. Ren, and Z. W. Ji, “A biological algorithm to solve the assignment problem based on DNA molecules computation,” Applied Mathematics and Computation, vol. 244, pp. 183–190, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  22. R. S. Braich, C. Johnson, P. W. K. Rothemund, D. Hwang, N. Chelyapov, and L. M. Adleman, “Solution of a satisfiability problem on a gel-based DNA computer,” in Proceedings of the 6th International Conference on DNA Computation (DNA '00), vol. 2054 of Lecture Notes in Computer Science, pp. 27–42, 2000.