Comparison of approximation algorithms for the travelling salesperson problem on semimetric graphs

TL;DR

This paper compares various approximation algorithms for the TSP on semimetric graphs, including a novel polygonal Christofides algorithm, through theoretical overview and numerical experiments to identify the most effective method.

Contribution

It introduces a new polygonal Christofides algorithm and evaluates its performance against existing algorithms via comprehensive simulations.

Findings

Polygonal Christofides algorithm shows competitive approximation ratios.

Numerical experiments identify the most effective approximation algorithm for semimetric TSP.

Comparison highlights strengths and weaknesses of each approach.

Abstract

The aim of the paper is to compare different approximation algorithms for the travelling salesperson problem. We pick the most popular and widespread methods known in the literature and contrast them with a novel approach (the polygonal Christofides algorithm) described in our previous work. The paper contains a brief summary of theory behind the algorithms and culminates in a series of numerical simulations (or "experiments"), whose purpose is to determine "the best" approximation algorithm for the travelling salesperson problem.