3D DNA self-assembly for maximum weighted independent set problem

The problem of finding a maximum weighted independent set (MWIS) is a classical combinatorial optimization problem of graph theory, which has been proved to be NP-complete (NPC). A 2-D DNA tile self-assembly model for solving the problem has been proposed previously, but it still has many deficiencies. In this paper, we will propose a 3-D DNA tile self-assembly model based on 2D DNA tile self-assembly model to solve the problem. This model includes two parts: the non-deterministic search system and the addition system. Firstly, we can find all the independent sets via the non-deterministic search system, and then get the total weight value of each independent set according to the addition system, and by comparison, the maximum weighted independent set will be found finally. Result shows that the operational time is linear, and the number of the tiles required in the process is constant.