A new DNA-based approach to solve the maximum weight clique problem

Given an undirected graph with weights on the vertices, the maximum weight clique problem is to find a subset of mutually adjacent vertices, i.e. a clique, which have the largest total weight. We devised a new DNA encoding method to solve the maximum weight clique problem whose basic idea is that each vertex on weighted graph is encoded by two DNA strands of different length and each edge is encoded by one DNA strand with a length of 20. The longer DNA strand corresponding to vertex v(i) consists of three parts and its center part is with a length of w(i); the shorter DNA strand is the reverse complementation of the longer one's center part. We also gave the correspond- ing molecule algorithm and its biological implementation. The proposed DNA computing method can be expanded to solve other NP-hard problems, and it provides further evidence for the ability of DNA computing to solve numerical optimization problems.