DNA Solution of the Shortest Path Problem by Concentration Control

DNA computing is the method for computation by using DNA and its chemical reactions. Adleman and Lipton have shown that an instance of NP-complete problems can be solved by DNA computing [1, 2]. Their methods first generate all candidate solutions in parallel, and then extract target DNAs by some chemical operations. However, such a simple approach to combinatorial problems will be unpromising, because the explosive increase of candidate solutions will be critical as the size of problem increases. In this paper, we propose a concentration control method for DNA computing. The concentration control implements local search for combinatorial problems, and enables us to handle optimization problems. Therefore, our proposed methods will be effective for solving more large-scale problems. In order to show the effectiveness of our proposed method, we demonstrate that the shortest path problem can be solved by DNA computing based on the concentration control.