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Minimum Finding with DNA Computing

Recently, DNA computing is one of powerful tools that can be designed for solving NP-complete problems. The powers of DNA computing are that it has great ability of massive data storage and it can process those data in parallel. Some of hard problems, such as the traveling salesperson problem and the Hamiltonian cycle problem, have been solved with the brute force method in DNA computing. After DNA computing is performed, all feasible solutions for the problem are stored implicitly in the tubes. However, the correct answer may not be extracted or reported easily, because that the concentration of the correct solutions might be lower. In this paper, we introduce some well-known experiment methods in DNA computing and solve the minimum finding problem with DNA computing. Our idea is based on the broadcasting scheme in a parallel system, which is a randomized scheme. In our method, some pilot numbers are selected randomly. Then, the numbers greater than one of pilot numbers may be deleted, and the numbers less than one of the pilot numbers may be amplified. This procedure is repeated until some predefined iterations are reached. Our method allows the chemical reaction error. Thus, our method is fault tolerant. Our idea can also be applied to many other DNA problem solvers.