A Molecular Computing Model for Maximum Independent Set Based on Origami and Greedy Algorithm

Maximum independent set problem has been solved based on a specially designed origami structure. In this model, greedy algorithm is applied to solve the problem. It only needs to generate initial graph but not the solution space. Every time we delete a vertex which has the most adjacent vertexes until a maximum independent set appears. Thanks to the special origami structure represented a vertex, it becomes very easy to determine a vertex connected most adjacent vertexes and to clear it up. This method will help to find the maximum independent set more quickly compared with traditional method (generate solution space). For a n-vertex graph, the time complexity is O(n(2)) at most. And its space complexity is O(2n) at most. This model demonstrates a great advantage to deal with similar problems.