In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a special form of reduction that uses a subroutine for the easier Linear Programming Problem only once. We use multiple calls to the subroutine increasing considerably the effectiveness of the reduction. Further the NP-complete problem we choose is also unusual. We define a special kind of acyclic directed graph which we call a time graph. We define Hamiltonian time paths in such graphs and also the Hamiltonian Time Path problem (HTPATH) and prove that it is NP-complete. We then state a conjecture whose proof will immediately lead to a polynomial-time algorithm for this problem proving P=NP.

翻译：本文提出了一种新的方法来构建P=NP的证明。我们建议将NP完全问题多项式归约到线性规划问题。早先的尝试采用多项式变换，这是一种特殊形式的归约，仅调用一次针对较易线性规划问题的子程序。我们通过多次调用子程序，显著提高了归约的有效性。此外，我们选择的NP完全问题也非同寻常。我们定义了一种特殊的无环有向图，称为时间图。在这类图中定义了哈密顿时间路径，并提出了哈密顿时间路径问题（HTPATH），证明了它是NP完全的。随后我们提出一个猜想，该猜想的证明将立即给出该问题的多项式时间算法，从而证明P=NP。