Application of 3D DNA Self-Assembly for Graph Coloring Problem

The tile assembly model has allowed the study of the nature's process of self-assembly and the development of self-assembling systems for solving complex computational problems. The design of large complex tile systems that emulate Turing machines has shown that the tile assembly model is Turing universal. Based on 2D extension of the tile assembly model, a 3D DNA self-assembly model for the graph coloring problem is proposed in this paper. Firstly, an algorithm for the graph coloring problem based on self-assembly is designed; secondly, a 3D DNA tile assembly system is designed to implement the algorithm. It's theoretically proved that the Tile system can determine arbitrary graph's k-coloring scheme, as long as it's k-colorable. The analysis shows that the tile types required in our model is independent to the size of the problem, and assembling time is linear. This study makes a significant attempt for exploring the computational power of 3D DNA self-assembly.