The k-vertex cover problem aims to find a vertex cover set with k vertices in a given undirected graph. Based on biological molecular computation, the paper describes a new DNA procedure to solve K -vertex cover problem in O n 2 time complexity, which greatly simplifies the complexity of the computation.

The maximum weighted clique (MWC) problem, as a typical NP-complete problem, is difficult to be solved by the electronic computer algorithm. The aim of the problem is to seek a vertex clique with maximal weight sum in a given undirected graph. It is an extremely important problem in the field of optimal engineering scheme and control with numerous practical applications. From the point of view of practice, we give a parallel biological algorithm to solve the MWC problem. For the maximum weighted clique problem withmedges andnvertices, we use fixed length DNA strands to represent different vertices and edges, fully conduct biochemical reaction, and find the solution to the MVC problem in certain length range withO(n2)time complexity, comparing to the exponential time level by previous computer algorithms. We expand the applied scope of parallel biological computation and reduce computational complexity of practical engineering problems. Meanwhile, we provide a meaningful reference for solving other complex problems.