Hard to Solve Instances of the Euclidean Traveling Salesman Problem
Discrete Mathematics
2020-03-18 v3 Computational Complexity
Data Structures and Algorithms
Combinatorics
Abstract
The well known conjecture states that the integrality ratio of the subtour LP is at most for metric Traveling Salesman instances. We present a family of Euclidean Traveling Salesman instances for which we prove that the integrality ratio of the subtour LP converges to . These instances (using the rounded Euclidean norm) turn out to be hard to solve exactly with Concorde, the fastest existing exact TSP solver. For a 200 vertex instance from our family of Euclidean Traveling Salesman instances Concorde needs several days of CPU time. This is more than 1,000,000 times the runtime for a TSPLIB instance of similar size. Thus our new family of Euclidean Traveling Salesman instances may serve as new benchmark instances for TSP algorithms.
Keywords
Cite
@article{arxiv.1808.02859,
title = {Hard to Solve Instances of the Euclidean Traveling Salesman Problem},
author = {Stefan Hougardy and Xianghui Zhong},
journal= {arXiv preprint arXiv:1808.02859},
year = {2020}
}