A new approach for a proof that P is NP

TL;DR

This paper introduces a novel approach to proving P=NP by utilizing multiple calls to linear programming subroutines on a specially defined NP-complete problem involving Hamiltonian time paths in acyclic graphs.

Contribution

It proposes a new reduction method using multiple linear programming calls and introduces the Hamiltonian Time Path problem, a novel NP-complete problem, as a key step towards proving P=NP.

Findings

Defined Hamiltonian Time Path problem (HTPATH) and proved NP-completeness.

Conjecture linking proof of HTPATH to P=NP.

Enhanced reduction technique using multiple LP calls.

Abstract

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.