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A DNA Algorithm for Calculating the Maximum Flow of a Network

Sackmann Andrea, Brown Kristelle, Formanowicz Piotr, Morgan Kevin, Kalsheker Noor, Garibaldi Jon M., Blażewicz Jacek

Foundations of Computing and Decision Sciences

2023

Vol. 48, No. 4

483--506

DNA computing is a highly interdisciplinary field which combines molecular operations with theoretical algorithm design. A number of algorithms have been demonstrated in DNA computing, but to date network flow problems have not been studied. We aim to provide an approach to calculate the value of the maximum flow in networks by encoding the mathematical problem in DNA molecules and by using molecular biology techniques to manipulate the DNA. We present results which demonstrate that the algorithm works for an example network problem. This paper presents the first application of DNA computing to network-flow problems. The presented algorithm has a linear time complexity where the calculation itself is done in a constant number of steps.