The application of fixed-length three DNA Segments encoding to maximum flow problem

Abstract

Fixed-length three DNA Segments encoding is brought forward. Therefore, closed circle DNA computing model is extended. The same position of extended closed circle DNA is divided into three sections corresponding to three function areas. The three function areas are addition segment, filling segment and subtraction segment, so extended closed circle DNA computing model can do addition operation and subtraction operation with simultaneous. For maximum flow problem, DNA algorithm is designed based on extended closed circle DNA computing model. In the DNA algorithm, fixed-length three DNA Segments encoding is encoded for flow rate of every arc, and all capacity feasible flows are formed. Then all feasible flows are filtered out by doing group insert experiment, group delete experiment and electrophoresis experiment. Using the same method all maximum flows are filtered out. Finally all maximum flows are obtained by doing detect experiment. Correctness and complexity of the algorithm are analyzed and proved. And a simulation experiment is done to verify validity of the DNA algorithm. This encoding mode is discovered firstly, and it is firstly using DNA computing from beginning to end to thoroughly solve maximum flow problem, so a conclusion can be drawn that the innovation of DNA encoding structure can solve more complicated and more extensive problems by DNA computing.