A novel computing model of the maximum clique problem based on circular DNA

A novel DNA-based model is developed to calculate NP-complete problems, which is made of circular DNA molecules, streptavidin-coated magnetic beads and DNA circligase. To test the feasibility of the model, we apply it to compute a five-node maximum clique problem (MCP). During the computation, DNA molecule structures were transformed between linear DNA and circular DNA by streptavidin-coated magnetic beads and circligase, in order to search for the truth solutions. This greatly reduces the quantity of time and space consumed in calculation, and its time and space complexity both are O(n+m). Compared with the brute force method, using this algorithm searching process at most needs in n + 1 test tubes for an MCP with n vertices, while brute force method requires 2n test tubes. Furthermore, the constructed unenumerable initial solution space greatly improved the processing ability of the DNA computer. This novel model indicates that it may be a powerful DNA-based computer for solving some NP-complete problems.

[1]  G Rozenberg,et al.  Computing with DNA by operating on plasmids. , 2000, Bio Systems.

[2]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[3]  Alessandra Carbone,et al.  Circuits and programmable self-assembling DNA structures , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[4]  R J Lipton,et al.  DNA solution of hard computational problems. , 1995, Science.

[5]  L M Adleman,et al.  Molecular computation of solutions to combinatorial problems. , 1994, Science.

[6]  J. Reif,et al.  Logical computation using algorithmic self-assembly of DNA triple-crossover molecules , 2000, Nature.

[7]  P D Kaplan,et al.  DNA solution of the maximal clique problem. , 1997, Science.

[8]  Chen Fang,et al.  Genetic algorithm in DNA computing: A solution to the maximal clique problem , 2004 .

[9]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[10]  T. Kasuga,et al.  Magnetic bead-isolated single-strand DNA for SSCP analysis. , 2001, Methods in molecular biology.

[11]  Jin Xu,et al.  A DNA computer model for solving vertex coloring problem , 2006 .

[12]  Yuriy Brun.  Arithmetic computation in the tile assembly model: Addition and multiplication , 2007, Theor. Comput. Sci..

[13]  Song Li,et al.  Multivariate refinement equation with nonnegative masks , 2006 .

[14]  J.,et al.  Using DNA to Solve NP-Complete ProblemsRichard , 1995 .

[15]  Raymond E. Miller,et al.  Complexity of Computer Computations , 1972 .

[16]  L F Landweber,et al.  Molecular computation: RNA solutions to chess problems , 2000, Proc. Natl. Acad. Sci. USA.