Unsplittable Euclidean Capacitated Vehicle Routing: A (2+ε)-Approximation Algorithm

Authors Fabrizio Grandoni, Claire Mathieu, Hang Zhou

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Author Details

Fabrizio Grandoni
  • IDSIA, USI-SUPSI, Lugano, Switzerland
Claire Mathieu
  • CNRS, IRIF, Université de Paris, France
Hang Zhou
  • École Polytechnique, Institut Polytechnique de Paris, France


We thank Vincent Cohen-Addad for helpful preliminary discussions. We thank the anonymous reviewers for their valuable comments.

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Fabrizio Grandoni, Claire Mathieu, and Hang Zhou. Unsplittable Euclidean Capacitated Vehicle Routing: A (2+ε)-Approximation Algorithm. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 63:1-63:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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+ε)-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].

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • capacitated vehicle routing
  • approximation algorithms
  • Euclidean plane


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