The Complexity of Euclidian 2 Dimension Travelling Salesman Problem versus General Assign Problem, NP is not P

TL;DR

This paper compares the Euclidean 2D Traveling Salesman Problem and the General Assignment Problem, highlighting polynomial-time verification for the former and addressing the NP vs P conjecture for the latter.

Contribution

It demonstrates polynomial-time solution verification for Euclidean TSP and discusses the NP vs P conjecture in relation to the General Assign Problem.

Findings

Polynomial-time verification for Euclidean 2D TSP.

Addresses the NP vs P conjecture for General Assign Problem.

Highlights differences between two NP problems.

Abstract

This paper presents the differences between two NP problems. It focuses in the Euclidian 2 Dimension Travelling Salesman Problems and General Assign Problems. The main results are the triangle reduction to verify the solution in polynomial time for the former and for the later the solution to the Noted Conjecture of the NP-Class, NP is not P.