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

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 on complete, weighted graphs.