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

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Abstract:

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.

Keywords: 3D DNA TILES; DNA SELF-ASSEMBLY; GRAPH COLORING PROBLEM; TILE ASSEMBLY MODEL

Document Type: Research Article

DOI: https://doi.org/10.1166/jctn.2011.1923

Publication date: 2011-10-01

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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