Molecular solutions for minimum and exact cover problems in the tile assembly model

The tile assembly model is a novel biological computing model where information is encoded in DNA tiles. It is an efficient way to solve NP-complete problems due to its scalability and parallelism. In this paper, we apply the tile assembly model to solve the minimum and exact set cover problems, which are well-known NP-complete problems. To solve the minimum set cover problem, we design a MinSetCover system composed of three parts, i.e., the seed configuration subsystem, the nondeterministic choice subsystem, and the detection subsystem. Moreover, we improve the MinSetCover system and propose a MinExactSetCover system for solving the problem of exact cover by 3-sets. Finally we analyze the computation complexity and perform a simulation experiment to verify the effectiveness and correctness of the proposed systems.