Asymptotic constant-factor approximation algorithm for the Traveling Salesperson Problem for Dubins' vehicle

TL;DR

This paper introduces the first constant-factor approximation algorithm for the Traveling Salesperson Problem with Dubins' vehicle constraints, achieving a performance bound of order n^{2/3} and bridging the gap between known bounds.

Contribution

It presents the first known algorithm with a constant-factor approximation for TSP with Dubins' vehicle constraints, improving upon previous bounds.

Findings

Achieves a constant-factor approximation for Dubins' TSP.

Closes the gap between lower and upper bounds for the problem.

Performance bound is of order n^{2/3}.

Abstract

This article proposes the first known algorithm that achieves a constant-factor approximation of the minimum length tour for a Dubins' vehicle through $n$ points on the plane. By Dubins' vehicle, we mean a vehicle constrained to move at constant speed along paths with bounded curvature without reversing direction. For this version of the classic Traveling Salesperson Problem, our algorithm closes the gap between previously established lower and upper bounds; the achievable performance is of order $n^{2/3}$.