A novel DNA computing model based on circular DNA length growth (CDLG) is developed to solve a maximal clique problem (MCP) with n-vertices. The time complexity of biological operations required is O(n+m) (m is the number of edges of the complementary graph), and the space complexity is O(n+m). The main feature of this model is using circular single-stranded DNA (c-ssDNA) to implement the computation on the nano-scale. By the CDLG method, the target DNA molecules will grow in length just when they satisfy the conditions. To verify the algorithm, a small paradigm is calculated by the nano-scale DNA computing model. The computing achievement by circular DNA demonstrates the potential ability of DNA computing to solve NP-complete problems.
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