A Constructive Algorithm to Prove P=NP

Abstract

After reducing the undirected Hamiltonian cycle problem into the TSP problem with cost 0 or 1, we developed an effective algorithm to compute the optimal tour of the transformed TSP. Our algorithm is described as a growth process: initially, constructing 4-vertexes optimal tour; next, one new vertex being added into the optimal tour in such a way to obtain the new optimal tour; then, repeating the previous step until all vertexes are included into the optimal tour. This paper has shown that our constructive algorithm can solve the undirected Hamiltonian cycle problem in polynomial time. According to Cook-Levin theorem, we argue that we have provided a constructive proof of P=NP.