A DNA length reducing computing model for maximum independent set problem

In this paper, a new molecular computing model is developed to solve the maximum independent set problem, based on the method of DNA length reducing. To solve the maximum independent set problem with n-vertices and in-edges, the time complexity is O(n+m). With the enlargement of the problem scale, the numbers of the required tubes will increase linearly. Two important methods in this experiment are single strand DNA (ssDNA) circularization and DNA length reducing. In addition, using reverse polymerase chain reaction (PCR) and circligase, the structure of DNA molecules is changed in each computing step, transforming from linear double strand DNA (dsDNA) to linear ssDNA and circular ssDNA. Using the circular DNA structure, the recombination among DNA molecules is avoided. To verify this computing model, a small maximum independent set problem was solved.