A Molecular Computing Model for Maximum Clique Problem Based on DNA Nanoparticles

In this article, the maximum clique problem is solved based on a computing model using DNA/AuNP (gold nanoparticle). In this model, the DNA probes are used to link the specific DNA/AuNP structures in order to generate initial solution space, then specific recognizing DNA/AuNP structures are used to delete the false solutions. Finally, the true solution can be separated by electrophoresis. Different from conventional algorithm, the algorithm in this paper has high efficiency as its low time and space complexity (both are O(2n+ m+ 2)). What's more, the biological operation is convenient and fast for it doesn't need any enzyme. Both the operations of eliminating false solutions and obtaining the optimum solution only need to be carried out once. This model presents a different method to solve similar problems.