# The Approximation Ratio of the Greedy Algorithm for the Metric Traveling Salesman Problem

arXiv: https://arxiv.org/abs/1412.7366 · HTML: https://mlsanity.com/paper/1412.7366/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2014.

## Built on by (most cited first, 2 of 2)

- [RedAHD: Reduction-Based End-to-End Automatic Heuristic Design with Large Language Models](https://mlsanity.com/paper/2505.20242/) (2025)
- [MOSAIC: Adversarial Co-evolution of Specialist Heuristics and Problem Instances for LLM-based Automated Heuristic Design](https://mlsanity.com/paper/2608.07544/) (2026)

## Abstract (arXiv)

We prove that the approximation ratio of the greedy algorithm for the metric Traveling Salesman Problem is Theta(log n). Moreover, we prove that the same result also holds for graphic, Euclidean, and rectilinear instances of the Traveling Salesman Problem. Finally we show that the approximation ratio of the Clarke-Wright savings heuristic for the metric Traveling Salesman Problem is Theta(log n).