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.