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Journal of Applied Mathematics
Volume 2013, Article ID 407816, 7 pages
http://dx.doi.org/10.1155/2013/407816
Research Article

Solving Vertex Cover Problem Using DNA Tile Assembly Model

Key Laboratory of Image Processing and Intelligent Control, School of Automation, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

Received 13 October 2013; Accepted 15 November 2013

Academic Editor: Sabri Arik

Copyright © 2013 Zhihua Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

DNA tile assembly models are a class of mathematically distributed and parallel biocomputing models in DNA tiles. In previous works, tile assembly models have been proved be Turing-universal; that is, the system can do what Turing machine can do. In this paper, we use tile systems to solve computational hard problem. Mathematically, we construct three tile subsystems, which can be combined together to solve vertex cover problem. As a result, each of the proposed tile subsystems consists of (1) types of tiles, and the assembly process is executed in a parallel way (like DNA’s biological function in cells); thus the systems can generate the solution of the problem in linear time with respect to the size of the graph.