A molecular computing model for 3-coloring graph problem based on circular DNA branch migration

A 3-coloring graph problem, one of the NP-problems, has been solved using the method of circular DNA displacement. The whole computing process is based on single circular DNA branch migrations just in a few tubes. For this computing model, two features are circular DNA and rather lower experimental complexity. Moreover, the key methods in this model include displacements of circular ssDNA (single strand DNA) and backtracking deletion algorithm. By repeating of DNA displacements, the correct solutions will be found after computing processes. For a 3-coloring graph problem with n vertices, using this algorithm, the time and space complexity both are O(n2) at most. During the computing course, an effective DNA strand displacement and exclusive sequence recognition ensure the accuracy of computing results. This model demonstrates circular DNA may have more applications in molecular computing.