Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm
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Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm

Authors Zipei Nie, Hang Zhou

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Author Details

Zipei Nie
  • Lagrange Mathematics and Computing Research Center, Huawei, Paris, France
  • Institut des Hautes Études Scientifiques, Paris, France
Hang Zhou
  • École Polytechnique, Institut Polytechnique de Paris, France

Funding

The work of the second author was partially supported by the Hi! PARIS Center.

Acknowledgements

We thank Claire Mathieu for helpful preliminary discussions.

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Zipei Nie and Hang Zhou. Euclidean Capacitated Vehicle Routing in the Random Setting: A 1.55-Approximation Algorithm. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 91:1-91:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ESA.2024.91

Abstract

We study the unit-demand capacitated vehicle routing problem in the random setting of the Euclidean plane. The objective is to visit n random terminals in a square using a set of tours of minimum total length, such that each tour visits the depot and at most k terminals.
We design an algorithm combining the classical sweep heuristic and the framework for the Euclidean traveling salesman problem due to Arora [J. ACM 1998] and Mitchell [SICOMP 1999]. We show that our algorithm is a polynomial-time approximation of ratio at most 1.55 asymptotically almost surely. This improves on the prior ratio of 1.915 due to Mathieu and Zhou [RSA 2022]. In addition, we conjecture that, for any ε > 0, our algorithm is a (1+ε)-approximation asymptotically almost surely.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial optimization
Keywords
  • capacitated vehicle routing
  • approximation algorithm
  • combinatorial optimization

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