On Polynomial Time Approximation Bounded Solution for TSP and NP Complete Problems

Abstract

The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in mathematics, computer science, biology, philosophy and cryptography. There are intensive research on proving `NP not equal to P' and `NP equals to P'. However, none of the `proved' results is commonly accepted by the research community up to date. In this paper, motived by approximability of traveling salesman problem (TSP) in polynomial time, we aim to provide a new perspective: showing that NP=P from polynomial time approximation-bounded solutions of TSP in Euclidean space.