Online TSP with Known Locations

TL;DR

This paper investigates the Online Traveling Salesperson Problem with known request locations but unknown arrival times, presenting algorithms and bounds for different variants and metric spaces to understand the impact of location knowledge.

Contribution

It introduces a 3/2-competitive algorithm for the general case and matching lower bounds, along with specialized algorithms for specific metric spaces.

Findings

A 3/2-competitive algorithm for the general case

Matching lower bounds for open and closed variants

Polynomial algorithms for ring, star, and semi-line spaces

Abstract

In this paper, we consider the Online Traveling Salesperson Problem (OLTSP) where the locations of the requests are known in advance, but not their arrival times. We study both the open variant, in which the algorithm is not required to return to the origin when all the requests are served, as well as the closed variant, in which the algorithm has to return to the origin after serving all the requests. Our aim is to measure the impact of the extra knowledge of the locations on the competitiveness of the problem. We present an online 3/2-competitive algorithm for the general case and a matching lower bound for both the open and the closed variant. Then, we focus on some interesting metric spaces (ring, star, semi-line), providing both lower bounds and polynomial time online algorithms for the problem.