The Computational Complexity of the Traveling Salesman Problem
Computational Complexity
2012-02-02 v6
Authors:
Craig Alan Feinstein
Abstract
In this note, we show that the Traveling Salesman Problem cannot be solved in polynomial-time on a classical computer.
Cite
@article{arxiv.cs/0611082,
title = {The Computational Complexity of the Traveling Salesman Problem},
author = {Craig Alan Feinstein},
journal= {arXiv preprint arXiv:cs/0611082},
year = {2012}
}
Comments
1 page, made a minor correction
Related papers
View all related →
Discrete Mathematics · Computer Science
A Polynomial Time Algorithm for The Traveling Salesman Problem
Sergey Gubin
2008-11-10
Computational Complexity · Computer Science
Analysis and Counterexamples Regarding Yatsenko's Polynomial-Time Algorithm for Solving the Traveling Salesman Problem
Christopher Clingerman, Jeremiah Hemphill, Corey Proscia
2008-01-04
Data Structures and Algorithms · Computer Science
Time complexity of the Analyst's Traveling Salesman algorithm
Anthony Ramirez, Vyron Vellis
2024-04-09
Data Structures and Algorithms · Computer Science
Classic Lagrangian may not be applicable to the traveling salesman problem
Michael X. Zhou
2014-05-07
Data Structures and Algorithms · Computer Science
A New Exact Algorithm for Traveling Salesman Problem with Time Complexity Interval (O(n^4), O(n^3*2^n))
Yunpeng Li
2015-10-16
Computational Complexity · Computer Science
Fast Exact Method for Solving the Travelling Salesman Problem
Vadim Yatsenko
2007-05-23
Data Structures and Algorithms · Computer Science
On Polynomial Time Approximation Bounded Solution for TSP and NP Complete Problems
Wenhong Tian
2016-12-20
Computational Complexity · Computer Science
The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme
Yair Bartal, Lee-Ad Gottlieb, Robert Krauthgamer
2016-09-09
Computational Complexity · Computer Science
A Conjecture Related to the Traveling Salesman Problem
Jian Yang
2023-04-24
Quantum Physics · Physics
Traveling Salesman Problem with a preprocessing method for classical and quantum optimization
Alessia Ciacco, Luigi Di Puglia Pugliese, Francesca Guerriero
2026-05-28
Data Structures and Algorithms · Computer Science
On Solving Travelling Salesman Problem with Vertex Requisitions
Anton Eremeev, Yulia Kovalenko
2017-03-14
Discrete Mathematics · Computer Science
Nonexistence of a Universal Algorithm for Traveling Salesman Problems in Constructive Mathematics
Linglong Dai
2021-08-12
Computational Complexity · Computer Science
The traveling salesman problem: A Linear programming formulation
Moustapha Diaby
2014-07-11
Soft Condensed Matter · Physics
Improving the Hopfield-Tank approach for the traveling salesman problem
M. Argollo de Menezes, T. J. P. Penna
2009-10-30
Computational Geometry · Computer Science
Approximation and Hardness of Polychromatic TSP
Thomas Schibler, Subhash Suri, Jie Xue
2025-07-08
Artificial Intelligence · Computer Science
Solving the Clustered Traveling Salesman Problem via TSP methods
Yongliang Lu, Jin-Kao Hao, Qinghua Wu
2022-04-15
Data Structures and Algorithms · Computer Science
Using a Hamiltonian cycle problem algorithm to assist in solving difficult instances of Traveling Salesman Problem
Vladimir Ejov, Michael Haythorpe, Serguei Rossomakhine
2017-05-22
Disordered Systems and Neural Networks · Physics
Phase Transitions of Traveling Salesperson Problems solved with Linear Programming and Cutting Planes
Hendrik Schawe, Alexander K. Hartmann
2016-10-18
Quantum Physics · Physics
Quantum simulated annealing
Steve Huntsman
2007-05-23
Optimization and Control · Mathematics
2-Period Balanced Travelling Salesman Problem: a polynomially solvable case and heuristics
Vladimir Deineko, Bettina Klinz, Mengke Wang
2022-03-14
Data Structures and Algorithms · Computer Science
Approximation Algorithms for the Traveling Repairman and Speeding Deliveryman Problems
Greg N. Frederickson, Barry Wittman
2009-05-28
Data Structures and Algorithms · Computer Science
Travelling Salesman Problem: Parallel Implementations & Analysis
Amey Gohil, Manan Tayal, Tezan Sahu, Vyankatesh Sawalpurkar
2022-05-31
Optimization and Control · Mathematics
Traveling salesman problem with time slots: Asymptotic analysis and resolution algorithm
Omar Rifki, Thierry Garaix
2023-03-27
Computational Complexity · Computer Science
A Reply to Hofman On: "Why LP cannot solve large instances of NP-complete problems in polynomial time"
Moustapha Diaby
2007-05-23
Computational Complexity · Computer Science
Report on article: P=NP Linear programming formulation of the Traveling Salesman Problem
Radoslaw Hofman
2007-05-23