# Edge Elimination in TSP Instances

arXiv: https://arxiv.org/abs/1402.7301 · HTML: https://mlsanity.com/paper/1402.7301/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Feb 2014.

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

- [Learning to Sparsify Travelling Salesman Problem Instances](https://mlsanity.com/paper/2104.09345/) (2021)
- [A New Constructive Heuristic driven by Machine Learning for the Traveling Salesman Problem](https://mlsanity.com/paper/2108.10224/) (2021)
- [Machine Learning-based Two-Stage Graph Sparsification for the Travelling Salesman Problem](https://mlsanity.com/paper/2604.20236/) (2026)

## Abstract (arXiv)

The Traveling Salesman Problem is one of the best studied NP-hard problems in combinatorial optimization. Powerful methods have been developed over the last 60 years to find optimum solutions to large TSP instances. The largest TSP instance so far that has been solved optimally has 85,900 vertices. Its solution required more than 136 years of total CPU time using the branch-and-cut based Concorde TSP code [1]. In this paper we present graph theoretic results that allow to prove that some edges of a TSP instance cannot occur in any optimum TSP tour. Based on these results we propose a combinatorial algorithm to identify such edges. The runtime of the main part of our algorithm is O(n2 log n) for an n-vertex TSP instance. By combining our approach with the Concorde TSP solver we are able to solve a large TSPLIB instance more than 11 times faster than Concorde alone.