# Hard to Solve Instances of the Euclidean Traveling Salesman Problem

arXiv: https://arxiv.org/abs/1808.02859 · HTML: https://mlsanity.com/paper/1808.02859/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Aug 2018.

## Built on by (most cited first, 3 of 3)

- [Improving Ant Colony Optimization Efficiency for Solving Large TSP Instances](https://mlsanity.com/paper/2203.02228/) (2022)
- [Revisit the Algorithm Selection Problem for TSP with Spatial Information Enhanced Graph Neural Networks](https://mlsanity.com/paper/2302.04035/) (2023)
- [Learning Lagrangian Multipliers for the Travelling Salesman Problem](https://mlsanity.com/paper/2312.14836/) (2023)

## Abstract (arXiv)

The well known 4/3 conjecture states that the integrality ratio of the subtour LP is at most 4/3 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 4/3. 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.