A new approach for a proof that P is NP

02/15/2023
by   Malay Dutta, et al.
0

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.

READ FULL TEXT
research
11/25/2017

Hamiltonian Path in Split Graphs- a Dichotomy

In this paper, we investigate Hamiltonian path problem in the context of...
research
04/28/2023

A Critique of Czerwinski's "Separation of PSPACE and EXP"

Czerwinski's paper "Separation of PSPACE and EXP" [Cze21] claims to prov...
research
05/13/2020

An improved solution approach for the Budget constrained Fuel Treatment Scheduling problem

This paper considers the budget constrained fuel treatment scheduling (B...
research
04/07/2021

On Salum's Algorithm for X3SAT

This is a commentary on, and critique of, Latif Salum's paper titled "Tr...
research
02/11/2020

A polynomial time parallel algorithm for graph isomorphism using a quasipolynomial number of processors

The Graph Isomorphism (GI) problem is a theoretically interesting proble...
research
12/29/2017

Interesting Paths in the Mapper

The Mapper produces a compact summary of high dimensional data as a simp...
research
10/18/2020

Solving Shisen-Sho boards

We give a simple proof of that determining solvability of Shisen-Sho boa...

Please sign up or login with your details

Forgot password? Click here to reset