Molecular Solution to Minimum Vertex Cover Problem Using Surface-based DNA Computation

The minimum vertex cover (MVC) problem is a classic graph optimization problem and has been shown to be NP-complete. For an undirected graph G, G = (V, E) where V and E represent the set of vertices and edges, the MVC problem is to find the smallest subset V*⊆V such that V* contains at least one of the two endpoints of each edge in E. This study finds molecular solutions to the MVC problem in three steps. In the first step, DNA strands are defined to represent the vertices; in the second step, the DNA parallel approach is adopted to construct the algorithm; and in the third step, the solution is read by fluorescence-image technique. The proposed approach applies mostly the surface-based computation model that was presented by Liu. The results demonstrate the capacity of molecular computing for solving the complex vertex cover problem.