# Probabilistic Analysis of Edge Elimination for Euclidean TSP

arXiv: https://arxiv.org/abs/1809.10469 · HTML: https://mlsanity.com/paper/1809.10469/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [Machine Learning-based Two-Stage Graph Sparsification for the Travelling Salesman Problem](https://mlsanity.com/paper/2604.20236/) (2026)

## Abstract (arXiv)

One way to speed up the calculation of optimal TSP tours in practice is eliminating edges that are certainly not in the optimal tour as a preprocessing step. In order to do so several edge elimination approaches have been proposed in the past. In this work we investigate two of them in the scenario where the input consists of n independently distributed random points in the 2-dimensional unit square with bounded density function from above and below by arbitrary positive constants. We show that after the edge elimination procedure of Hougardy and Schroeder the expected number of remaining edges is Theta(n), while after that the non-recursive part of Jonker and Volgenant the expected number of remaining edges is Theta(n2).