# 5/4 approximation for Symmetric TSP

## TL;DR

This paper introduces a new heuristic called 2 RNN for symmetric TSP, achieving a proven approximation ratio of 5/4, improving upon the longstanding 3/2 ratio by Christofides.

## Contribution

The paper presents the 2 RNN heuristic and provides both experimental and theoretical analysis confirming a 5/4 approximation ratio for symmetric TSP.

## Key findings

- Experimental results support the 5/4 approximation ratio.
- Upper bound analysis confirms the heuristic's approximation ratio.
- The heuristic outperforms previous approaches in certain cases.

## Abstract

Travelling Salesman Problem (TSP) is one of the unsolved problems in computer science. TSP is NP Hard. Till now the best approximation ratio found for symmetric TSP is three by two by Christofides Algorithm more than forty years ago. There are different approaches to solve this problem. These range from methods based on neural networks, genetic algorithm, swarm optimization, ant colony optimization etc. The bound is further reduced from three by two but for graphic TSP. A factor of thirteen by nine was found for Graphic TSP. A newly proposed heuristic called 2 RNN is considered here. It seems from experimental results that five by four is the approximation ratio. Upper bound analysis for approximation ratio is done for this heuristic and it confirms experimental bound of five by four.

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Source: https://tomesphere.com/paper/1905.05291