Unsplittable Euclidean Capacitated Vehicle Routing: A $(2+\epsilon)$-Approximation Algorithm

TL;DR

This paper presents a polynomial-time algorithm that approximates the unsplittable Euclidean capacitated vehicle routing problem within a factor of 2 plus epsilon, improving previous approximation bounds in the Euclidean plane.

Contribution

It introduces a $(2+ ext{epsilon})$-approximation algorithm for the Euclidean case of the unsplittable capacitated vehicle routing problem, advancing the state of the art.

Findings

Achieves a $(2+ ext{epsilon})$-approximation in polynomial time.

Improves upon recent approximation bounds by prior researchers.

Specifically tailored for the Euclidean plane setting.

Abstract

In the unsplittable capacitated vehicle routing problem, we are given a metric space with a vertex called depot and a set of vertices called terminals. Each terminal is associated with a positive demand between 0 and 1. The goal is to find a minimum length collection of tours starting and ending at the depot such that the demand of each terminal is covered by a single tour (i.e., the demand cannot be split), and the total demand of the terminals in each tour does not exceed the capacity of 1. Our main result is a polynomial-time $(2+\epsilon)$-approximation algorithm for this problem in the two-dimensional Euclidean plane, i.e., for the special case where the terminals and the depot are associated with points in the Euclidean plane and their distances are defined accordingly. This improves on recent work by Blauth, Traub, and Vygen [IPCO'21] and Friggstad, Mousavi, Rahgoshay, and Salavatipour [IPCO'22].